Okay, I'll fess up - this isn't a post about how to use "Sailing to Byzantium" as game inspiration, though I've done that too. I recently read The Grand Strategy of the Byzantine Empire by Edward N. Luttwak, and (like anyone as monomaniacal as I am) I reinterpreted a lot of what he talks about through a gaming lens. Before I really dive into it, let me recommend the book in the strongest available terms: if you care about a more nuanced understanding of medieval warfare and politics, or if like me you previously knew approximately nothing about the Eastern Roman Empire, this book is ideal.
(For clarity, I'll generally be calling them Byzantines rather than Eastern Romans. I know perfectly well that this is historically laughable.)
It was Dust to Dust that first got me interested in the Byzantine Empire. One of the ancient cultures, which I called Tharicia in a conscious allusion to Thrace, was supposed to be "a Rome that was never sacked, that survived into the Middle Ages and even into the beginning of the Renaissance." Kainenchen picked up the task of writing the culture packet for Tharicia, and took the whole thing in the direction of the real-world Rome-that-never-fell, right next door to Thrace... exactly what I had described, but didn't know I was describing, because I really was that ignorant of the tone and style of the Byzantine Empire. (In my defense, we were spinning out a whole hell of a lot of setting in a hurry - I didn't have time to think it through that far. Fortunately, K did.) The deeper I got into Luttwak's book, the more impressed I was with the work K had done on the culture packet.
As I've mentioned before, my first tabletop game and earliest experience of D&D were Second Edition. Countless gamers sing the praises of the 1e DMG; I don't think I go too far to say that it is the most famous book on game-running ever written. It wasn't my foundation, though, and I've still never read it more than superficially. It was Zeb Cook's 2e DMG that I pored over throughout middle school and high school. Since you surely have a copy of that distinguished tome near at hand just as I do, turn to page 108... wait, there was a reprint in '95? Your copy uses different pagination? Dammit!
The point I'm making is that the chapter on hiring soldiers puts a lot of its focus on the arms and armor of Byzantine troops and the various peoples they fought. Western Europe and early-Renaissance Europe aren't completely ignored, but Constantinople (including Varangian Guardsmen!), Persia, Pechenegs, and other Turkic peoples get a huge share of the focus. (Never knew what the hell a Pecheneg was? I sure didn't, until Luttwak explained it to me.)
Digression time: The obscurity of many of these references highlights to me that, as the tabletop gaming population has grown up, we've collectively shifted from kids reading rulebooks written by geeks, in a time when geeks were rare and marginalized, to adults reading books written by peers, when geeks have come into their own. Also, the completely human-centric and Eurocentric approach that the developers took in the chapter on soldiers would never fly in any later edition. (Human-centric here is well-justified - the text is only intended to provide examples for inspiration.)
Also, I don't pretend that drawing gaming inspiration from the Byzantine Empire is a new idea. A cultural cognate of the Byzantine Empire was a central part of the world-history of King's Gate, and I seem to recall that the Empire of Warhammer 40K is Byzantine in derivation. (Which shows you just how little I know about WH40K, but I digress.)
The important thing is, I knew next to nothing about the Byzantine Empire, and now I'm talking about it with the fervor of the converted the college student who just learned about this awesome new thing for the first time. (Usually these are Philosophy majors.) What I learned from The Grand Strategy of the Byzantine Empire is that Byzantium, anywhere from A.D. 400 to 1204, would be an absolutely phenomenal setting or source material for a campaign. Alternately, of course, all of these features mean that you can build a great campaign on playing non-Byzantines seeking the Empire's demise. This book just isn't as much help with that perspective. Let me call out some of the salient points:
Constantinople is surrounded by fallen empires. You think Forgotten Realms is lousy with ruined kingdoms and civilizations? Rome goes from "crumbling" to "sacked" in 476, having long since withdrawn from its most distant holdings in Britain, Gaul, and so on. Western Europe is littered with Roman villas and fortifications to explore - this is pre-medieval-post-apocalypse.
Closer to home are the ruins of Ancient Greece, still seen as the bright torch of scholarship - enough so that plagiarizing or, more rarely, paraphrasing a Greek text is academic authority, rather than sloth. Introducing arcane scholarship into this world is the smallest imaginable step, as they already looked to the past for secret wisdom in exactly the manner that Vance's wizards seek to recover lost spells rather than develop new ones.
Anatolia (Asia Minor), Constantinople's own back yard, has ruins of unbelievable antiquity. If your interweb habits are anything like mine, you've seen a whole lot of collections of awesome Anatolian archaeology photos over the past few years. The greatest of these is, of course, Cappadocia.
Not too far distant from Asia Minor is Mesopotamia, one among several places commonly called The Cradle of Civilization. So, you know, probably a pretty decent supply of ruined empires. Also, from a Byzantine perspective, it's a primary warzone in the on-again-off-again conflicts with Persians, Arabs, and Turkic peoples. This is the territory you defend so that you don't have to fight them on the Bosporus or from the walls of Constantinople.
The Byzantine Empire goes through countless cycles of growth and collapse in the 800-year span I've mentioned, often reaching exceptional zeniths and nadirs within the reign of a single emperor. These dramatic reversals provide grist for as many missions behind enemy lines and daring raids as one could want, all without leaving the comfort of Thrace.
Interesting Approach to Enemies
One of the most surprising things I learned from the text is that the Byzantine Empire generally did not put its full effort into killing its enemies. Given the choice between a costly battle that might wipe an enemy from the face of the Earth or a war of relational maneuver that would kill far fewer people and expose the Byzantine force to less risk, they consistently chose the latter. If they had an enemy who could be bought off, they bought them off, time and again. The reasons for this are particularly compelling:
Byzantine military tactics, whether infantry, cavalry, or navy, required an absolutely colossal amount of training, so they had to maintain the soldiers as a standing army more often than not, and casualties were very difficult to replace. This contrasted sharply with the wars of attrition that the Western Roman Empire favored, as Western Rome had a realistic hope of incorporating their enemies into the empire as Eastern Rome did not. This is compelling in a game environment because it values smaller numbers of incredibly elite forces over larger masses of manpower - giving PCs a greater personal role in the outcomes of battles.
Decisively defeating an enemy today means that you can't hire them to fight another of your enemies next year. The Byzantines seem to have understood that neither alliance nor enmity was a permanent state, and planned accordingly. Also, there will always be more horse-mounted archers coming from the steppes in hordes to attack the Empire. Without exception. Some centuries have more capable and cunning hordes than others, but if your enemies are without limit, you've got to find a way to turn some of them into allies. This is compelling in a game environment because it rewards more nuanced solutions to problems than genocidal warfare. It also addresses, without exactly resolving, some of the problems around finding a Fun Game Experience in ethnically delineated warfare.
If yours is the only economy and source of finished goods for a few thousand miles in any direction, giving the Enemy of the Year gold and silver in exchange for leaving you alone for another year takes on a completely different character. They're going to spend it on things your populace makes, and you tax that income quite efficiently, so it's more like an economic stimulus package than a loss of face. (Luttwak makes the point that the Byzantines had a better tax-collection infrastructure than any other empire of its day or earlier.) I would find it fascinating in a domain-level game if paying off your enemies had a good chance of resulting in an economic boom in the threatened province.
This also means that a human-only campaign set in a fantasy version of the Byzantine Empire would still have a wide range of ethnic groups and backgrounds for characters, without having major problems cooperating in a team of three to six. That's more... just how life was. Dynasties change all the time - if you go into the military or civil service, you might be able to make the right connections to get yourself appointed as the next emperor. Be very careful about this; in many eras of the empire, it is a death sentence.
Okay, Greek Fire has been hugely mythologized, when in reality its creation was widely known not only in the Empire, but to the Empire's enemies as well. This is a piece of historical accuracy that you can throw out the window in the name of fun, or you can embrace the massive proliferation of a highly flammable, mass-produced liquid. If you can't get some fun action sequences out of that, I don't know what to tell you, friend.
Christianity is the state religion, but that doesn't mean things are calm on the spiritual front. Regardless of the fact that Constantinople is the seat of spiritual authority that hasn't fallen to the barbarians in this time period, it is still overshadowed by other cities of antiquity in honor and spiritual authority. Christianity is also very much in flux during the early centuries of the Byzantine Empire, and the Council of Chalcedon created a schism within the faith that persists to this day, though I doubt most Protestants or Roman Catholics have even heard of this schism - I know I hadn't.
Even discussing real-world religious conflict can easily become incredibly uncomfortable for people, though, so I'd recommend only exploring this if you're completely sure of your players' responses, or if you're drawing a veil of fantasy-setting distance over the whole thing. For example, Forgotten Realms is literally named for its many, many crumbling empires - so playing a historical piece set in one of them and basing it on the Byzantines might provide a fresh approach to the setting. In that case, you could probably have a lot of fun with a religious schism over something that seemsincredibly obscure, but gets the religious leaders riled up.
You can be a chariot-racing hero, showered in fame and glory, and it's a politically-relevant part of gameplay. Everyone in Constantinople is wearing the jersey of their favored team. How cool is that?
Also, more than one of my friends will fucking knife me if I write a whole post about the Byzantine Empire without at least a passing reference to how cool Theodora was.
I've always been a big fan of basing game cultures off of real-world cultures, because I like getting (or giving) a little bit of a history lesson along with fun gameplay. Even if you don't go that far, I feel like it can't hurt to learn how Eastern European medieval warfare was conducted, because a whole lot of us have learned only the stories of Western Europe - Tours, Stirling Bridge, Crecy, and Agincourt come to mind. The Byzantines had a completely different approach to exactly the same technology as a result of different enemies and terrain, and that's fascinating in itself.
One last thing. You thought Pendragon's 80-year Great Campaign was a long haul? At one year per session and one session per week, the Byzantine Empire would last you fifteen and a half years.