If you are looking for some culture then check out the Denver Art Museum (
http://www.denverartmuseum.org/) and/or the Denver Museum of Nature and Science (
http://www.dmns.org/) who I believe has a Maya exhibit going on right now. They are both rad and fairly cheap.
For food, bars and music there is plenty of action down in Lodo.
If you want skate spots in the city I would say just look around, I don't go downtown a lot but, in my experience there are plenty of decent spots but not a whole lot of "you gotta hit this one up" type of spots. 303 might be able to help you out
http://303boards.com/. Also the new Null "Nothing" video is a good way to up your Denver/Boulder/Suburbs stokeage...
If you can manage to hit up some parks in the suburbs I strongly recommend Lafayette (
http://www.coskate.com/SkatePark.aspx?Park=COLafayette), Arvada (
http://www.coskate.com/SkatePark.aspx?Park=COArvada) and Northglenn (
https://www.northglenn.org/skatepark). They are really fucking nice but try to avoid Lafayette at peak times when school is out because it's notorious for scooters and van loads of kids.
If you want to make fuck with nature then there are a lot of good little hikes in the Foothills this time of year. West and Northwest from Denver, just look for trails out in Golden or Eldorado Canyon or head into South Boulder and hit NCAR or Chataqua.
I'd offer myself up to tour guide but I am pretty jammed up this weekend through Tuesday. I am open during the week though if you need somebody to show you around or take you to some lower key skate spots, just send me a PM.