I didn't make it all the way up to Steamboat, but I was in Vail/Edwards last week. We had hopes of fishing the Eagle river but due to snow melt it wasn't an option. We used Vail Valley Anglers for 2 days and fished on our own for 2 days(highly recommend them). We drove up to Stagecoach Reservoir on one of our off days, which is about half an hour south of Steamboat. If you get there early enough, you can fish Yampa creek on the east side, or keep driving down CR-18 to Sarvis creek. It was 4th of July week so it was fairly crowded so we had to go to Sarvis to avoid the crowds. We caught some nice Rainbows and Brook trout.
On our guided days, we started at Pump house campground on the Colorado (about an hour and half south of Steamboat). The rivers south were so blown out from the snow melt we had to hit the bigger rivers. The first day we waded north of Pump house about a mile and had really good success with some PMD emergers (pinkish). Two days later we did a float trip from Pump house south about 6 miles and landed well over 30 fish, most in the 16-20" range. If you decide you want to do this, ask for Andy Jackson at VVA, can't speak highly enough about him.
Yampa Valley Anglers is another one that has good reviews and I believe is based out of Steamboat. As we left the Vail Valley, river flows were starting to really come down 200-300 cfs/day, so conditions should be improving. While crowds from the holiday weekend should reduce, we spoke to several locals who stated that due to the rivers they haven't been out yet, so that might pick up as river conditions improve.
Best of luck, and keep me posted on how you do.