Red Cliff has good riding. It is basically the same as what you get from Vail Pass. There is not much parking there, so you need to know someone, set something up with Mangos or the Green Bridge Inn. I haven't been to Mangos in a while and ownership/management has changed a couple times. They used to be great. I can also vouch that the Green Bridge Inn, is nice. Clean rooms, very modern, cool place. You can get to Camp Hail, Vail Pass, Ptarmigan, Lime Creek, etc etc. Riding from the Red Cliff side can get sketchy in the Spring because the town plows up to the water tank to give them access for water maintenance for the town. About 2.5 miles of road that maybe mud or very thin snowpack. Sometimes you can ride the snowbank down. Middle of winter it will be a snow packed road. It is still a fee area at the lower "gate" or where the Lime Creek road is accessed from the bottom. If you know where you are going you can access a lot of riding pretty easily from Red Cliff. There is some patches of private around the town that you're not supposed to access. You can get to Minturn, you can get to Fremont pass pretty easily, Homestake.
Depending on where you are coming from you might be ahead to go to Vail Pass. If you're coming from Denver, just start at the top of VP. Leadville, I'd go to Camp hail. If you're coming from the other end it could be sixes on where you go in at.
But to the OP, Red Cliff is nothing like Yellowstone.