I think I know which apts you're in, and you could have done a LOT worse.
Being on top of the Belleview light rail station is the shiznit, head to downtown for all your partying needs without the parking hassle or DUI fear. Local brews can be found at
Baker St. Pub (walking distance in good weather), and you have the Greenwood Village shops/movie theater/etc right down the street off of Quebec. There you'll find a smattering of upper-scale restaurants (including a really good sushi place, Happa) and a Landmark Theater.
You're in a great spot. As far as riding is concerned, you can head south really easily (I use Monaco to Orchard to Colorado, that's my commute when I ride). And Cherry Creek Res is literally off of Union (head over the highway and keep going till you pass the high school; you're there. To get to the mountains on bike from where you are, I'd head south (either via the Highline Canal Trail, or Colorado) and hop on the C470 trail and head west. You are about 15mi or so from the mouth of Deer Creek Canyon, a popular climb (I'm leaving the politics out of this).
Denver is great, you will be quite pleased--