This time of year, a lot of the mountain streams are frozen over. Even many of the ponds and lakes down here in town are a bit tough to get a fly through the thick surface film. The South Platte has some great fishing and lot of it is only a half hour or so from anywhere in the Metro area. Some of it is right in town!
These folks have been a BIG help to me and have referred a lot of repair work and a couple of builds my way. They are stand up folks. http://www.fortackle.com/Guided-Fly-Fishing-Trips-.html The shop is literally a block from the river. Ask for Cody. He's one that can help.
These guys are big on the South Platte and can put you onto some big fish without much of a drive from town. They also know where the open water in the area is. I don't know them as well as I do the other guys, but I have been to the shop and talked with them a bit.
www.coloradoskiesoutfitters.com
I might add that a lot of really pretty country is not far away at all from downtown Denver. Even the tail waters of the South Platte below Chatfield Reservoir are nice in most places. Between 11 Mile Reservoir and Chatfield is a lot of Gold Medal water. A bit more of a drive, but well worth it.