There are great trails everywhere. In no particular order: Crested Butte, Durango, Vail, Salida, Gunnison, Fruita, Moab UT, Telluride, Aspen, Summit County, Colorado Trail and so on.
Help us help you by letting us know your athletic ability (for climbing), endurance level (for trail length), and skill level (for technical ability). Some areas have more of one type of riding than other so one destination might be better for you than another.
Also, when do you plan to visit? With the snow we are having this winter, it is doubtful that the highest alpine rides will be open before mid-July (401, Monarch Crest, ****, Two Elk). Fruita and Moab are not the best places to be in June-August unless you're disciplined about water intake (and if you ride really early or late).
Good luck
GS_Ken
Glenwood Springs, CO