I have now read up to the end of Book 3 of A Song of Ice and Fire (both parts), which I continue to think of as Game of Thrones. I haven't read any of Book 4 yet, though, so please, please, don't mention anything that happens after the end of Book 3 in the comments - not even vague allusions to what happens (e.g. I knew one character death in advance because of the facial expression Brother pulled when I said something, which was entirely my fault for insisting on talking about it). I just got past all the spoilers I'd already picked up! This post contains spoilers up to the end of Book 3.
Fantasy novels, for reasons best known to CS Lewis and JRR Tolkien, are usually set in a pseudo-medieval pseudo-Europe. When the time comes to travel south, there are two main options; medieval Arabia, as seen in Arabian Nights (and the Chronicles of Narnia), or the Classical world, particularly the Roman Empire and Roman Africa (Tolkien went for a variant - the southern parts of his fantasy world are loosely reminiscent of Byzantium, the Eastern Roman Empire that continued after the fall of the West until the Turks conquered Constantinople in 1453). Elements of Ancient Egypt are optional.
The Roman Empire seems a particularly natural fit for A Song of Ice and Fire, since George RR Martin's fantasy world already incorporates elements of the Roman Empire in the wall that separates Westeros from the distinctly Scottish-accented Wildings* (I am most disappointed that the TV series has so far continued with Northern English accents for the wildlings, but perhaps some of the more northern Thenns and so on will have Scottish accents in season 3).
The lands south of Westeros (actually east, maybe south-east of the more northern parts of Westeros - but they feel southern) are, as usual, made up of a mixture of elements. There are elements of Arabia in there, especially in some of the names, while the Dothraki horse lords seem like a cross between the Klingons and the Rohirrim (I'm sure they have a real life parallel, but I'm not familiar with it). There is also, though, quite a lot of Classical stuff, and it's an eclectic mix.
Perhaps surprisingly, there's more Classical Greece in the Lands of the Summer Sea than Roman Empire. There are several city-states like Meereen and Astapor, which provides a big advantage plot-wise, as it allows Daenerys to conquer a whole city-state relatively quickly, in one siege. This matches the political landscape of Classical Greece, with surrounding farmland etc, but the entire population taking refuge in the city when under attack. King Cleon, the butcher-king of Astapor, is named after Cleon, an Athenian general who was popular with the masses and something of a war-monger (with an occasional habit of executing lots rebels en masse), referred to as a tanner by Aristophanes because that's where his family's money came from. There are also several references to Greek mythology. The harpies that are the emblem of Meereen are particularly Greek, though here they're mixed with a Great Pyramid that's obviously inspired by Egypt.
In terms of the action taking place in the south, though, we're back to Rome again, as Dany's modus operandi is to free large numbers of slaves and get them to fight for her. In real life, in the ancient world, slave rebellions were extremely rare and the three largest all happened within a few decades of each other, in the south of Italy, in the Late Roman Republican era (which would imply that there may be other socio-politico-economic factors at play beyond just the desire on the part of slaves to be free). Daenerys' conquest of at least two city-states fits that pattern quite nicely, as it's her political agenda and her money (well, her valuable dragons) that are the driving force behind the revolts. Dany's strategy at Meereen would be unlikely to work in the real world because it involves large numbers of slaves being inside the city, when normally slaves would be most numerous outside in the fields and the mines. Having said that, there must have been a lot of slaves in Athens when everyone was sheltering there during the Peloponnesian War, and presumably quite a few slaves in Rome during major Games, so it might have been possible in a Classical context (even if no one actually did it).
The most satisfying aspect of this plotline so far is that we start to see the long-term results of these revolts. Daenerys herself is against slavery as a concept (and the Unsullied are a particularly nasty variant, far nastier than anything I've come across from real life). However, the rest of the people she conquers and even the slaves are not, which fits with the slave revolts from the ancient world - Spartacus wasn't trying to end slavery, he was just trying to escape himself (with his own people). After Dany has swept through and turned the world upside down, behind her things start snapping back into place, and she realises that if she wants to make a lasting difference, she has to stay and rule in person.
I'm sure there were lots more Classical references scattered throughout the book, but it's such a very long book it's rather difficult to remember them all now! One of the most popular elements of ancient Rome for fantasy writers is gladiatorial-style contests, and there are definitely a few of those in the southern/eastern/hot areas. I expect as we see more of the Summer Isles and the Lands of the Summer Sea in the following books, we'll get more Classical references and Classics-y stories.
My review of Game of Thrones, Season 1
*Yes, I am aware that at the time of the Roman Empire, Scotland was inhabited by Picts and Ireland by Scots.