Sounds like maybe a family vacation and you're hoping to fish a little? Every stream in the park will have fish. Browns, rainbows and brookies. Bigger water, bigger fish and vice versa. Probably the best chance for a biggun would be outside the park on the Big Thompson, but...it gets hammered.
If native trout interest you, there are greenback cutts on the east side, and Colorado River cutts on the west side of the divide. Lily Lake used to have a lot of greenbacks, but that population has taken a few hits in recent years. It's easily accessible, and therefore gets pressure. You can also get greenbacks along Roaring River at Aspenglen Campground and upstream. CO River cutts are rare, and I can't post what I know on a forum. I'll just say they get outcompeted by the brookies and interbreed with the rainbows, so go up, up, up to find them.