I never see much love for A-Basin on this forum, but when I went to school in CO it was my favorite. Great steep terrain and a much smaller, fun vibe. Perhaps it was because I tele skied at the time - maybe people will comment that it is not great for boarding. But, given that you are going to spend some significant time, I would try to hit them all. You aren't going to really get to know a mountain in that time so just enjoy exploring. Breck, Keystone, Copper, and A-Basin are all within about 30 minutes and I imagine you can catch a bus to all of them even if you don't have a car.
If you really take enough time you can hit Vail and/or Beaver Creek just to see another mountain. All of those resorts are easily accessible if you are staying in Breck or Frisco/Dillon/Silverthorne.
Others can comment with more specific info, but my suggestion would be to go for the variety and see it all. Have an awesome trip!