Thats interesting......Good luck do it. Lets think it through.....you take a pick up or suv you can sleep in and carry your gear. The summer is like mid june to end of aug minus 2 weeks to get to college so your talking like 6-8weeks. To drive and camp you looking at like 1day travel, 1 day to camp at like a camp ground. 1 day hike in camp, 1 full day in the wild, hike out back to camp 1 day so like 5 days per location. So in 7 weeks you could do like 10 locations.
So you need rations you can carry in to the wild for 14 days(3meals ?7$x 14d=?300).
11 full tanks of fuel. (20gx3:00$/gx11d=660)
20 days of camp ground fees.(20dx15$pd=300)
food for camp (park)and travel days 36dx2mealsx10$=720
sleep 10 days in you car first nigh in town-$0
So high estimate: Throw in some entertainment and hike fees fire wood, call it $2500/50 days.
So where you gonna go 10 locations: yosemite, grand canyon, bryce,crater lake, yellow stone, zion, sonoma, lake tahoe, rockies somewhere, glacier, And Id blow anything I have left with a big finish in vegas.
God I wish i was going with you. Don't get lost or die.