I live in Woodland Park and am well familiar with the roads you'll be taking.
You'll be on U.S. Highway 24 heading west out of Colorado Springs. You'll pass by Manitou Springs and Cascade and through Woodland Park and Divide before turning south on CO highway 67 to go to CC. Highway 24 is four-lane divided highway from Colorado Springs to Divide. You'll gain about 3000 ft elevation by the time you reach Divide. That stretch of road is called Ute Pass but it doesn't really compare to a lot of the mountain passes in Colorado. It's a fairly gradual climb with a few moderately steep stretches but nothing serious. The first few miles, from Colorado Spring to Cascade, is 45 mph twisting road that's very scenic. After Cascade there's a bit of a climb for a few miles but the road is fairly straight. Woodland Park is at 8400 ft elevation and the highway takes you right through the town and several traffic lights. Past that it's another few hundred feet up in elevation to Divide (about 9000 ft). Between Divide and Cripple Creek on highway 67 is very scenic, lots more twists and turns, and another 500 ft of elevation gain.
If your GPS alternatively takes you past Divide on Highway 24 and has you turning on Teller County road 1 in Florissant, the road between Divide and Florissant is also fairly scenic with lots of curves and reduced speed. Teller 1 is a decent road but you'll do a bit of climbing as you get close to CC.
All these roads get a significant amount of RV traffic. Highway 24, in particular, is the main route to western Colorado from the Springs, and RV traffic is considerable during the summer--especially afternoons around the weekend. Try to avoid Friday afternoon going westbound, and Sunday going east. The traffic is manageable but you might find that getting through Woodland Park on a Friday afternoon will take a little extra time. Traffic returning to Colorado Springs on Sunday afternoon can also experience significant backups. If you have to travel during peak times, just pack your patience with you.