On $85/day for two people . . . let's be sure I understand: $85/day must cover your living expenses, and you have "extra money" for fun stuff, touristy stuff. So we only need to address the living expenses.

An RV is totally impossible. That budget won't even cover the cost of the rental, much less gas, mileage fees, and campsite rental. And that leaves you nothing for food.

I don't know how feasible it is to buy a car, then sell it right away.

I checked a SMALL RENTAL car (two people, I figure a compact Chevy Cobalt will do, and they get decent mileage) from Avis rented from June 1 - August 31, and it cost (including taxes, etc.) $25/day.

Mixing things up isn't really an option. First, renting anything one-way is extremely expensive. Second, unlike European countries, we don't have a plethora of convenient trains, and in all honesty, our busses aren't all that safe. Cheap, yes. Safe, not so much. If you're going to check into these options, our train system is called Amtrak, and our busses are called Greyhound. You can google information on them. America's size and geography really dictate that for such a trip, having your own transportation is the only realistic option.

Wait, I just realized a problem: Are you coming back to the North /East to fly home? If you're planning a one-way trip and expect to fly home from California, then you'll not get a rental car for $25. It'll be considerably more.

If you rent a car, that leaves you $60/day for two people -- tight, but do-able. A campsite will average $20/night. If you camp, however, you'll probably need to pick a slightly larger vehicle (to accomodate a tent, sleeping bags, and more), and that'll raise your car rental. Hotel rooms vary widely by cost; some are as low as $40; others are in the hundreds. Priceline is a great source for low-priced hotels.

Gas is about $2/gallon in most places.
If you were to start in New York, to go Miami, then end in San Francisco, you'd travel 4333 miles and would use about 144 gallons of gas at a cost of just under $300. This would require about $4/day from your budget.
If you're making a loop trip and are returning back to New York, it'd be more like 7242 miles, 241 gallons and just short of $500, $5.50/day from your budget.
Of course, this is a VERY rough guess, and I"m making some BIG ASSUMPTIONS here: You said North East and I guessed New York. You said California, and I chose San Fran ramdomly. Also, this doesn't allow ANY getting-lost miles or driving around town miles -- you should probably allow another 30% for that, just to be safe. Finally, will gas STAY at $2/gallon? Who knows? This time last year it was $4/gallon, and it could return to that price literally overnight. I think it'd be safer to assume $3/gallon, and know that IF it doesn't go up, you have a little extra spending money.

With so many variables, I'm not sure I answered any questions whatsoever.