Kit over on the DWAITAS board mentioned the possibility of a game set around Gallifrey. I think too much time spent there takes away its sense of mystery and wonder, making it too much like a hybrid of Westminster and Cambridge. (And if I want to run that, I had a Buffy game set in Cambridge already.)
There is a lot of Douglas Adams's Cambridge experience in the makeup of Time Lord society, but it also gave us the Doctor and the Master, much like Cambridge gave us the Cambridge Four as well as its more "normal" graduates. It's a hotbed of great thinking as well as an institution of arcane tradition, as much a home to those determined and brilliant enough to get in as those privileged enough to make the cut through family and school connections. And there's the town as well as the gown - even in the citadel, there are still normal Gallifreyans (and quite possibly other species) working in the guard towers and the kitchens. An "Upstairs, Downstairs" game with them could be interesting too.
And for a game focusing on the wildly inventive side of the Time Lords, world-saving craziness mixed with intellectual snobbery, check out SHIELD from Marvel Comics, which reveals the mad science secret history of the Marvel Universe and sets Galileo against Galactus. The portrayal of Newton could certainly make a suitable basis for a scheming Time Lord politician.