In Winter it seems you'd want to be up in Beaver Creek for the skiing, but in summer this is a great choice. We're staying in the villa's and can literally walk out of our door and fish in the Eagle River. Our first day we saw a fishing tour being taken there, so it certainly rates.
Several mountain bike rental shops around. We chose Venture Sports with good prices, bikes and a willingness to negotiate (if, for instance, you're renting multiple days during your stay).
Maya restaurant in the Westin is top rated - we enjoyed it but service was surprisingly slow. At one point in the evening everyone around us was sitting impatiently waiting for their food. Slow dining Mexican? I think not.
Hiking - many options. A short nice loop from Beaver Creek takes you through the "Aspen Glade" trail which is extraordinary. Highly recommended. Easy to spend a good part of the day in Beaver Creek. A beautiful spot with creek running through, trail, bridges, outdoor dining and much more.
Gym/pool/hot tubs - I was quite impressed by the gym. Fantastic facility, spinning classes, yoga and everything you'd hope for. i worked out most days but didn't have time for any classes, though I wanted to try spinning/pilates. Not sure if there's an extra charge if you're a hotel guest as opposed to gym member. The pool was nice for an evening dip, but we would have enjoyed the hot tubs if they were hotter - more like luke warm tubs :-)
Overall a great visit and I'm sure I'll be back.