I stayed at the Clyde Holliday State Park, water & electric with bathrooms & showers. Be sure to stop at the Kam Wah Chung State Heritage Site in John Day, although it is a bit east of the 3 parts of the National Monument.
Some photos from my visit.I've also stayed at the Wheeler County RV Park in Fossil. Closer to the Clarno unit of the park, but a typical city campground - water & electric, bathrooms with showers. An interesting very small town - check out the museum - the only place I've see a gasoline powered iron!
If you do a Google custom search from my
home page (scroll down) for John Day, you can find links to a couple of visits to the area.
And, while the John Day Fossil Beds National Monument is in Oregon, I'll second a visit to the City of Rocks State Park in New Mexico. Camping among the rocks is neat!