Colorado is a great place for golf, and some amazing weather that time of year (May/June) and if you play up in the mountains you'll notice how the altitude gives you some distance.
Fossil Trace is a fun course to play once, but it's not something that I'd want to play every week. It's tricked up but in great shape. Worth it for the rock formations and coolness factor, but not a place for scoring. Vail Golf Club has some amazing altitude changes, and you get to walk through Vail which is pretty cool. It's about 1.5-2 hours from Denver. I used to live 5 minutes from Keystone and Breck, and both those courses are nice, but nothing that will really blow you away for the price. You pay for the views once you get into the mountains, and they're some pretty great views, but typically golf courses as Colorado goes. If you do go to Keystone or Breck, there's a ton of really cool places to eat and grab some micro-brews in both Dillon (Keyston) and Breckenridge. Definitely worth it if you're in the area not trying to squeeze in 36 a day or something.
If you want to go on the cheap while you're in Denver, City Park is a muni course right in the middle of the city (across from the zoo). Best kept muni course I have ever played in my life. Very straight forward course, but if you just want to sneak out for a quick round while in town it's not bad at all, and they make a good breakfast sandwhich in the restaurant.
If you're dying to play the second you get off the plane, you can hit a bucket, or play a round, at Green Valley Ranch which is right off Pena Blvd (the only road to DIA). I've stopped there a few times on my way back to the airport if I'm running early to hit a bucket.
Like MEfree said though, I'd wait until June to play any course in the mountains (Keystone, Vail, Breck) just so the courses are in good shape and you don't risk any snow, although I did hear it's been light this year.