Jeez - I always thought Denver was a weak copy of LA, but with no In-N-Out Burger. Hope you're not disappointed.
There are some new-ish, nice art galleries and a bunch of kinda nice restaurants in LoDo, which is within walking distance from the Brown Palace. Actually, LoDo can be a nice half-day of shopping/eating. Denver's laid out in a clean, solid, grid, so you can just walk all of downtown without necessarily having much of a plan.
The art museum is being a little too discreet about upcoming exhibits, and the performing arts center is real quiet in the summer.
Even non-baseball fans seem to enjoy a Rockies game at Coors field, which is also a short walk from your hotel.
If you do rent a car, you can come up here and visit me in Boulder - about 25 minutes away. The summer's great here, and you can easily spend a full day shopping, eating, museuming, visiting the
tea house, stuff like that.