What do you mean by "in the general area?"
Vail is sort of between Holy Cross and Eagle's Nest wildernesses on this map:
So you're also near Mt Massive, Hunter-Fryingpan, Flat Tops, and Maroon Bells. Well, actually the last two are a bit west on 70, but totally doable if you'll have a car, and I've heard great things about them both. (They are on my list for this summer.) A good chunk of the CT is just south of Vail, too, IIRC.
Or do you want hikes you can just walk to from Vail?