I camped at Mitten View back in the 90s and although crowded it provided great access to MV. My favorite place to camp in the area is Goose Necks State Park near Mexican Hat,perched on top of a mesa overlooking the San Juan River. It's extremely windy late afternoon until late at night. It used to be a primitive cg with pit toilets near the entrance and no defined camp spots as you drove to the very end of the mesa. Great views and a great hike down to the river.
I've driven through MV on several trips and never get tired of it. On my wife's first trip there in 2000, we did the drive, plus we took a jeep tour which takes you off the main road where our guide drove us to pictoglyphs, sweat lodges,and some locals' homesteads. Well worth the tour!!
Have a great adventure!!