Most of Colorado fits your high altitude definition, and you've already got several excellent suggestions for rides here. There are several week long supported tours through the state, mostly through the mountains, that provide lots of clean, fresh, bracing air as well as breath-taking riding and scenery. The tour organizer will carry your gear, provide aid stations, and organize food and lodging; and you just ride your bike on well marked routes for a week. These include Ride the Rockies, Bicycle Tour of Colorado, Colorado Rocky Mountain Bike Tour, and 109 West Bicycle Tour. There are probably others.