If you want to tour Dinosaur National Monument in summer, it will be HOT! We arrived around 4 pm when the temperature was close to 100 degrees. Here's the (minor) problem with Green River Campground in the Utah portion of the park: there's not much shade.
But you may be able to get a site with some shade. How? Loop B's sites (23-55 among 80 total sites) are reservable between mid-May and mid-September. For a possibility of shade in the late afternoon/early evening, try for 23, 30, 32, 37, 39, 42, 49 or 55. (Some photos are included.) 30 and 42 are good for a group that needs two sites.
We wanted to stay two nights and considered going the walkup route, but we weren't sure if the walkup sites in loops A and C would fill up. (FYI they didn't fill up on Tues/Wed night.) We reserved a site in loop B for one night because that's all we could get. We planned to get in early and transfer to a walkup site where we could stay for two nights. The host was amenable to that, and she encouraged us to search for a shady site.
The search for shade is a good reason for moving if you have a reserved site with little to no shade. Loop C had some good possibilities among the cottonwoods. So.....reserve a site, get in early and move to a (somewhat) shady site.
Other than the lack of shade and abundance of heat, the campground was fine. One minor gripe: the bathroom has water and soap but no paper towels or hand dryers.
Looking at fossils: It's not easy to find fossils on the 1.2 mile hike between the Visitor Center and the Quarry Exhibit Hall. After we went out on our own, we realized a ranger-led hike would have been better. Before or after, you will see plenty of dinosaur bones in the Exhibit Hall which is a building that encloses an excavated area.
Hiking: The hike above the Green River between the Green River and Split Mountain (group) campgrounds is beautiful...and hot. There are other hikes listed in a brochure you can get at the entrance or Visitor Center.
Something we didn't know until we arrived: To see the Colorado portion of Dinosaur National Monument, you have to drive back to the town of Dinosaur CO (30 minutes) and enter the park north of there. There's also a campground over there.