A Living Room, the Campus of a Small New England College
Albee gives no description in his stage directions as to what George and Martha's living room might look like. Martha gives us a pretty big clue, though, not long after she first enters the stage. She walks in, scans the room, and says, "What a dump" (1.10). George talks a little trash about it too, saying it's okay for Nick and Honey to throw their coats on the "furniture" or "floor" because, it "doesn't make any difference around this place" (1.169). We also know that George is only an associate professor and therefore doesn't make a lot of money. All these things lead us to imagine that the room is pretty shabby and probably reflect the decaying state of George and Martha's marriage.
We also know that the house is on the campus of a small New England college. The fact that George and Martha live on campus shows that they're both firmly under the thumb of Martha's father, who is the president of the university. It's also interesting that Albee describes it specifically as a small college. This makes George look like even more of a flop, as he can't even move up in the ranks where there's undoubtedly less competition than there would be at a large university. It also makes Martha's worship of her father seem more pathetic.
George dubs the town they live in "New Carthage." There's a possibility that this isn't the real name. It could just be another history joke on George's part. Even if this isn't a joke from George, it's certainly a historical allusion from Albee. Back in the day, Rome was at war with a city-state named Carthage. This famous conflict is called the Punic Wars, which George also makes reference to specifically at one point in the play. Rome eventually obliterated Carthage, leveling the city, killing everybody in it, and sowing salt into the soil so crops could never grow again. The fact that George calls his town New Carthage could mean several things. Perhaps it reflects his wish that his town be obliterated as well. It could also reflect the overall fear pervasive in Cold War America had of being annihilated by a nuclear holocaust. For more on the Cold War references, check out "Symbols, Imagery, Allegory."