Going to Italy for a week this summer. Anyone have any tips?

I'm planning on going to Italy this summer (sometime after June 6 and before Aug. 1).  I want to go for about 7-10 nights and of course see as much as I can in that time.  I want to set a tentative budget for $1500 (is this realistic?).

Does anyone have any tips/websites on:
1. Cheap airfare or cheap dates to travel
2. Top things to see.  I'm trying to go to Rome, Florence, Venice, and maybe Milan.
3. Recommend staying in Rome for all 7 nights or switch between hotels and stay in a few different cities for the 7 nights