Mineral Basin is directly behind (west) of Princeton, between Cottonwood and Tincup Passes. It has no road over the CD so much less traffic. The FS has recently improved the road so you can get to ~11,500 w/o problems. The dispersed camping starts ~1-mile west of the Cottonwood Lake CG and follows the road, FR344, all the way to MB. The higher you go, the fewer the people.
If you get a chance, hike the new CD trail, goes from Cottonwood Pass to Emma Burr Mtn. There are no signs and few access routes, but it is worth the bushwhack. It varies from 11,900 to 12,800 just below the ridge, amazing trail engineering. Just go west from 344 and you'll stumble upon the trail. At the north end of MB, the CD trail crosses over to the Gunnison side of the CD, spectacular. Look for goats on the ridges.