ADenver: Places of Interest
You should try Ophelia's Electric Soapbox, Coors Field, and The Source.
ADenver: Short, scenic drives from Denver?
The drive up to Estes Park is a can't miss (take the route through Boulder, Nederland (Colorado), Allenspark on the way there and head back through Lyons).
ADenver: Where to Stay to Get a Feel for Denver Life
$1,200 or less for rent is going to be tough. You should look at staying some place close to LoHi or Uptown - both are excellent options!
ADenver: Colorado Trip in Mid May
Definitely check out Steamboat Springs, but it's going to be mud season there in May.