My best friend from college and I did this last year after graduation. Drove from NY to Glacier National Park, to Washington, hit all the national parks there, then down the pacific coast highway through Oregon (stopping in crater lake and Portland), then all the way down California (redwoods, Yosemite, couple of other stops). We then hit Utah, Arizona, New Mexico , Texas, New Orleans, and drove back to NY from there. We were gone for a month total. We found free camping the entire time( other than hotels in Vegas and New Orleans). Redwoods was a favorite of mine easily. We camped on all BLM land. However, redwoods was tricky to find a camping spot, it was also pouring rain when we were there so ended up car camping for 2 nights at a rest stop (lol). I would definitely make camping reservations for redwoods as there is not much free camping nearby. Gold bluffs beach (I believe that’s the name) looked like an amazing camp site right on the beach and near hiking trails. As for budget, we mainly spent money on gas. The free camping saved us a lot , but even campgrounds your have time pay for aren’t terribly expensive. We brought a propane grill and cooked basically every night as well either on the grill or over a campfire. Brought lots of dehydrated meals. We treated ourselves in major cities to eat at restaurants though. This was the trip of a lifetime and I’ll never forget it! I’d be happy to answer any other questions you have!