For any Estes Park/Rocky Mountain National Park fishing, I recommend cheching in at Kirk's Fly Shop first. Those guys know the park, and fish it daily.
Here's a link to their weekly fishing report, but I recommend stopping in Kirks. Pick up some flies, check out their shop, and ask them for advice. [log in for link]
As for the hike. It's steep the first mile. Up switchbacks. You'll see the river after about a mile, then walk in sight of it for a half mile. When you first see it, you're well above it on an eroded cliff, and they dicourage people from cutting down, as it will add to the erosion. That is probably the dangerous river bank you heard about..
The fish are quite small, but are pretty. In the lake itself they're bigger, but that's a day hike..
The water is ice cold, but I wouldn't lug waders up..
Have you considered some of the park lakes? Dream is only a mile hike, and you'll pass by two other lakes. The Cutts you'll catch there aren't big either, but larger than from the River..
Good Luck, and remember to check park regs. Hooks have to be debarbed, and fish returned to the water immediatley. Handle the Greenbacks as little as possible.