I vote for Breck also
For summertime, Breck is a great place and there are so many things to do in the general area. There are numerous timeshares in Summit, but I have to agree that Hyatt Main Street, Valdaro, Grand Timber and Gold Point are all very good. These are mostly II, so if you are looking for RCI - French Ridge is just ok. If you get a remodeled room, French Ridge can be very nice. I wrote a very detailed review of French Ridge from our 2008 stay over the 4th of July.
Swan Mountain is also very nice and they are also RCI. They are actually closer to Keystone, but it is all so close to each other it does not make much difference. We prefer biking in Keystone, fishing in Lake Dillon and you can hike anywhere.
Steamboat is beautiful, but Breck would get my vote due to the variety of things to do in Summit County.
I am not a huge fan of Vail, summer or winter. I know that I am in the minority with regards to winter due to the terrain for skiing. But, Vail just is not favorite for many reasons.
You will not go wrong with Breck, do the summer thing on the mountain (Alpine slide, maze etc..) you can hike, bike (paved trail along the Snake River or of course down the mountain), horseback ride, shop, white water raft, go fishing, do the gold mine tours, go golfing, get a massage or other spa treatment, history tours, take scenic drives, or did I mention just relax!
Breck also has great restaurants - from gourmet to inexpensive burgers or pizza.
Everyone goes to Colorado during the winter to ski, but I actually think the Summer equals or surpasses the winter vacation. The summers in Colorado are nothing short of wonderful. We could spend the entire summer there - if only someone would pay our bills!
You will enjoy yourself regardless of which you choice, Good luck!