It is possible to travel by bicycle from Meeker Park to Estes Park by following four-wheel-drive roads through National Forest lands behind the Twin Sisters mountains. This is an interesting trip that provides good altitude training, since it requires some 1500 feet of elevation gain. The route begins from Cabin Creek Road, which turns east off Highway 7, south of Estes Park, at Mile 11.5 in Meeker Park.
After turning onto Cabin Creek Road, follow the dirt road until it ends at a T junction; turn right at the T, following Cabin Creek eastward for about a mile. Then the road turns to the north and there is a sign about National Forest access. A map and compass (as well as some water -- none on route) are probably a good idea. There are markers along the road; in general, keep to the left at intersections and head north. The route takes you uphill to House Rock and Pierson Park. There are some barbed-wire fences that may need to be opened and re-closed.
After the top of the route, the road is downhill, sometimes steeply, most of the rest of the way. Use caution when there are washboard ruts across the road, since these can cause loss of control at higher speeds. The route will come out near the intersection of Fish Creek Road and Highway 7, near Cheley Camp. From there, one can go up onto Highway 7 and then into town via Highway 7 or Mary's Lake, or continue down Fish Creek Road and come out at Lake Estes near the high school.
This route is well suited to mountain bikes, although I have always done it on a road bike. You should be prepared to be relatively self-sufficient, since there isn't much traffic on this road.