I'd recommend the Four Pass Loop near Aspen. It's 26 mile loop that crosses four high passes and puts you near a bunch of 14,000+ foot peaks (Maroon, N. Maroon, Snowmass, Pyramid). Trails Illustrated 128 (Maroon Bells) covers the whole loop. If possible, go during the week to avoid (some of) the crowds. This has been a low snow year so far in CO so the passes might be snow-free in mid-July but it wouldn't hurt to bring an ice axe and know how to use it.
[Edit: Drink beers at Aspen Brewing Company after the trip.]