Goblin Valley SP is no where near Canyon of the Ancients NM. Here's a second vote for McPhee Reservoir. Quite near the Anasazi Heritage Center where they can give you good info on other sites to visit like Sand Canyon and the various parts of Hovenweep.
If you really want to boondock, try heading north out of Dolores on 526 (11th Street). After a few miles, there are a variety of roads off the road in both directions with camping spots. Do a little research with satellite images on Google maps or the like to scout out where you want to go ahead of time. For instance, check out some of the spots here: 37ยฐ32'33.2"N 108ยฐ27'25.0"W Or look along 529 and 528 in this area.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)