Yep, go for the Greenback or Colorado River cutts if you’re interested in rare, beautiful, native trout. Greenbacks are on the east side of the divide, and the easiest place to get to them is where Roaring River dumps into Fall River at the alluvial fan near Aspenglen campground. Colorado River are on the west side and you’ll have to hike up higher to get to them. Otherwise, brookies, browns and rainbows live in every stream or lake in the park. Check the regs—there are some areas with special restrictions.
Not familiar with Glenwood Springs area.
RMNP is stunning scenery, good wildlife watching and decent fishing. Be sure to go through the park, and up over the divide. Early in the morning or in the evening are best for avoiding traffic and crowds and seeing wildlife.