There is always Northern New Mexico. Much closer to you. And then there is Ashley National Forest in Utah, otherwise known as the Uintas. You have the Wind Rivers in Wyoming, which are almost as far as the Sawtooth, just a little closer.

All places will have their busy areas and their isolated areas. Generally, the farther away from a car, the more isolated. But if there is an attraction (like a specific peak) there might be a lot of people trying to get to it.
For example, in the Uintas, there is King's Peak. It is 2 days from a car. However, if you are between the peak and the parking lot....lots of backpackers. If you go past the peak or even left or right of the area between the cars and the peak... no one. Very interesting.