Summit county is about an hour and a half drive from Denver (except on friday evenings or saturday mornings, when the traffic gets bad).
Summit county is made up of 3 main towns that are not ski areas; Frisco (this is where I lived when I lived out there), Dillon and Silverthorne, which are all right next to each other. Then there are the the ski areas in Summit County; Breckenridge, Keystone, Copper and A-Basin. Breckenridge is also a real town, and Kestone is sort of a real town, but has no real walking village like Breck has. Copper is building up it's twon, but I haven't been there in ages, so others will know better. It's about 6-9 miles (10k ish?) from Frisco, Dillon, Silverthorne, to any of the Summit County ski areas. Vail as about a half hour drive west. Within 2 hours you could be at Steamboat, Winter Park, Aspen, Loveland (You'll literally drive UNDER loveland ski area as you drive to Summit County from Denver. You go through a giant tunnel in the mountain (Eisenhower Tunnel), and the ski area is on both sides and on top of the tunnel). Dillon and Silverthorne are literally next to each other. Only seperated by when you go under Interstate 70. Frisco is on the other side of Lake Dillon, but only 2 miles away.