I currently live in Madison and have lived here for many years. The Williamson St./ Schencks corners area has a high concentration of grad students. It's on the near east side. Downtown has many yuppies and grad students, stick to the north and east sides of the capital,the south and west is almost all undergrads.
$1200 is more than enough for a decent apartment. Where are you going to be working?
Ford's Gym is the only powerlifting gym around. I have never been in Monkey Bar, but I think it's only bodyweight stuff and maybe kettlebells. I don't think they have barbells and dumbells. Princeton Club has pros and cons, what are you looking for?
Feel free to send me a PM if you have any other questions or post them here.