I second Breckenridge... wife and I stayed there last July and had a fabulous time. Breckenridge is a great town and pretty much the entire town is in walking distance from the Hyatt. It is also a real town... we drove to Vail and Beaver Creek and while they are both beautiful they are resorts, not towns.
Also the Breck gondola is free in the summer unlike Beaver Creek/Vail which can save a lot of money if you want to ride up and hike, bike, visit the fun park etc.
Also Copper Mountain is close by to Breck and they also have a lot of fun stuff for kids and the cost is very reasonable for a day pass to ride as much as you want.
I highly recommend Kayak Lake Dillon and for horseback riding Gore Range Outfitters!