We live in the Denver Area and do have to compete with a lot of people coming from elsewhere. You will find that many campgrounds get reserved up as soon as the reservation windows open - usually 6 months in advance. National Parks fill up especially fast and State Parks on the weekends. So you do have to plan ahead.
Dinosaur - Can be very hot in July and August. Several commercial campgrounds are in Vernal. The only one we have stayed at is the KOA, which was OK. There are a couple of
Steamboat Springs - Tends to fill up. Steamboat Lake is a popular campground but needs reservations. There are a couple of commercial parks. KOA west of town is tight. Eagle Soaring RV Park, a bit further west looks like its nice but we have never stayed there.
Grand Lake - Good entrance to RMNP West Side. West Side tends to be less crazy than the east side, but you do have to drive over Trail Ridge Road to get to east side hiking. Timber Creek campground on the west side is first come first served. They lost their trees due to beetle kill, so not much shade unless you bring your own. A couple of commercial RV parks in the area. Elk Meadows is just outside Grand Lake. Also quite a few campgrounds around Lake Grandby
Boulder - Busy, Busy, Busy. I don't know of any RV Parks right there. Stop at Avery Brewery
Garden of the Gods - A couple of commercial RV parks around, but they aren't too highly rated. I recommend MountainDale which is about 20 miles south of Colorado Springs. Its about half way between Colorado Springs and Canon City. Makes a really good base camp to go to either place. We've been to MountainDale several times and you need to reserve ahead to get spots in the trees.
Canon City - Several commercial parks in the area, but I'd recommend stating at Mountaindale. Its about 30 minutes to Canon City
Gunnison - Not real familiar with the area. There are a couple of campgrounds on the reservoir east of town. Black Canyon of the Gunnison NP is an hour or so drive. There are campgrounds at Black Canyon, but they don't allow generators. Camping in Montrose is available also, which is a shorter drive to Black Canyon.
Ouray - Wonderful little town. There are a KOA and I think an RV Park at the hot springs. Ridgway State Park has a nice campground about 20 miles from Ouray. Day trips to Silverton, Teluride and similar spots.
Cortez - Cortez can be very hot in the summer. There is a campground in Mesa Verde that generally has availability. Also Mancos State Park is nearby. Also consider a day trip from Durango to MVNP.
Durango - If you are taking the train up to Silverton make your reservations well ahead if you want one of the more comfortable ($$) cars. Good idea to reserve ahead for anything. There are a couple of RV Parks in Durango, one of which sits right off the Durango and Silverton tracks so you can watch a dozen steam trains a day. If you are in Mancos its an easy day trip. If you take the train, I recommend taking the train up to Silverton and the bus back. We got stuck with the train both directions and its a very long slow trip back.