If you happen to visit RMNP here is some information you might want to read: Fishing - Rocky Mountain National Park
Just below Estes Park is the Big Thompson river, lots of public access along the hwy, but it can get busy especially on weekends. Another thought would be to hit the Poudre River just above Ft Collins. Hwy 14 runs along the river for the entire length and there were numerous campgrounds. I haven't been there since the big fire which took out some of those campgrounds, but I have heard that the fishing is still pretty good. Another idea would be to fish the Colorado River west of Granby on hwy 40 toward Hot Sulpher Springs to Parshall. There are a number of public access points and some allow camping. To get there you would take I-70 west out of Denver, then turn off on hwy 40 between Idaho Springs and Georgetown and follow that toward Hot Sulpher Springs and you will see the public access signs. The hot springs would be a good stop to soak in the warm pools after a long day of fishing.