Probably my all-time favorite place to explore. It is located about 10 minutes SouthWest from Gunnison, Utah (about 5 minutes directly West from Centerfield, Utah). Lone Cedar Canyon road connects Centerfield, Utah with Scipio Lake. As a kid I spent hours either alone or with friends exploring this area, both on four-wheelers and on foot. Locals refer to the area as the "West Hills." There are some peaks, I don't know if they have any names. The highest reach around 7,200 feet or so. There are lots of areas to get great views of the Gunnison Valley, and lucky explorers can find an old shack with a small abandoned gold sluice.
Lone Cedar Canyon Road is the main road across the mountains. Other than Lone Cedar Canyon Road, there are a few four-wheeler trails. Not a lot of people visit the area so there are very few single track trails to follow. Trails aren't needed however, because the undergrowth is not thick and it's pretty easy to just make your own trail through the cedar trees and desert scrub. Once you get off the main road, it is extremely rare to see another person while you are there exploring.
If you are looking for a place where you can be alone, then I recommend checking out Lone Cedar Canyon.