RED ROCKS
You would do best to go to the Gallery as there are lots of fun sport climbs there and almost always people so you shouldn't have a problem catching a ride. The Gallery is on the right side of the road that loops through the park.
"But what is happiness except the simple harmony between a man and the life he leads?" – Lord Byron
There is a one way road thru RR. Stop by the visitor's center to get some general info on the place itself. Once you leave the vc, you will pass a couple of pull-offs on your right. There is climbing out of both of these, the Gallery is out of the second pull-off. Might try a couple of spots at the first pull-off too. You should be able to see people at these areas from the road. Watch for burrows!
I see they are still lopping off mountains in Eastern Kentucky. Electricity isn't cheap.
The visitor center will give you an ok climbing guide for a day or two's worth of climbing. Hit the main areas at both the second and the first pull-out. I would also hit the Calico Basin area, and if you take a pad with you hit Kraft boulders. All the areas will be packed with climbers and tourists. Hit them as early as you can and you will be able to have some time alone.