If you want to explore Denver, pretty much any of the 3 GA airports near town are fine (KAPA, KBJC and KFTG - Listed from busiest to least busy and most amenities to least amenities). You should call ahead, but I don't think you'll have trouble getting transportation. Once in Denver, the RTD trains/buses will get you where you need to go (check out the RTD Trip Planner on their website).
If you want to fly your bird around the area, I'd recommend heading west, for some mountain flying, to Steamboat Springs, Gunnison or Leadville (highest public airport in North America). If you don't want to fly into the mountains, you could head south to Colorado Springs for nice flights near Pike's Peak, continue on to Pueblo, for a nice Aviation Museum visit, head northwest to Boulder for a nice short flight, or farther north up to Fort Collins. Google is your friend, for things to do, and there's lots to do here.
P.S. Just please don't encourage any more people to move here, okay?
