It'll be hot, but don't even waste any time in the East central areas (IMO...lived in NY though so done lots on the East. Drove X-country 3 times though. Look at some images at
www.greene-art.com) Head over to the 4 corners area (Utah, AZ, CO, NV). Tons of great red- rock areas, lakes, dams, Grand canyon.
Or if you prefer the cooler MTNs, go Northernly and hit glacier NP, and farther North to the Canadian Rockies....amazing. Of course Idaho is amazing to drive thru and then you can meander around WA state. Olympic NP, Mt Rainer, head south, Mt Baker (or is it Adams?), Mt St Helens...keep going south and you get Crater Lake in OR, Canon Beach in OR (and or Ecola state park). More south in to CA and you have the Redwoods, Pacific Coast, Mt Shasta, & Lassen Volcanic NP. More of a mid states route and you got Yellowstone and the Tetons too.
Been a while since I looked at a map or took a trip out of AK but you'll need to decide what route your gonna take and then narrow it down from there. There are TONS of amazing places to go!
Camping gear takes space? All you really need is a small sleeping bag and maybe a bivy sack. Breakfast on granola bars or protien bars and eat a "real meal" after some good early morning hiking and photography back "in town"!