Have you been to visit Cambridge?
If you're looking for central, then I would advise you not to go too central because it's full of tourists!
I imagine there are alot less tourists during term time, but all the same...
Clare, King's, Trinity, Trinity Hall, Gonville and Caius, Queen's, are all central, with Gonville and Caius being the most central I can think of. It's right by the market, if I remember correctly.
You may want to cross off Girton, Churchill, Selwyn, St. Catherine's and Homerton straight away, as those aren't very central (but Cambridge is very small, so it's really not far at all).
Clare, Trinity, Trinity Hall, are all extremely pretty. In fact, Trinity Hall is this tiny little college, with a tiny little courtyard, with lots of prettiness!
Feel free to disregard all of this, as I am not a student, and this was based on just 2 days in Cambridge.
I can give you more information on Churchill though.
It has huge grounds, with a very climbable tree (more of course, but we fell in love with just one).
The rooms are nice!
The gym is well equipped.
PAV SOUNDS AMAZING.