Jerry's point about HGI's is a good one: since that's a relatively new brand, you will get a lot of clean, new buildings - in many cases priced only a few bucks above a Hampton.

Since the OP is roadtripping across the country, I assume he's doing a mix of rural/city stays, not just all rural. In that case, it's an even stronger recommendation for sticking with HHonors, as you'll probably want to "move up the chain" a notch or two in a bigger city. (The cleanest Hamptons are the rural ones.)

TTT's point about s-l-o-w earnings at Fairfields is true, but if you're going soon you could hit Marriott's Megabonus promotion, which is 5,000 points for every three stays. But given the existing HH Gold status, I'd probably just go with HHonors.

I'd highly recommend getting a AAA membership. Aside from the obvious benefits related to the roadtrip itself, it will almost always save you a few bucks a night at Hampton Inn. AAA rates are available at almost all HHonors hotels, but higher up the chain it's hit-or-miss whether it's really the best rate vs. the other promo rates available. At Hampton, it generally is the best publicly-available rate.