If you're gonna pay for flights in the US, hotels, taxis and other transportation to get around, then I'd consider the small RV option for sure. You'll have to do the math on costs, but for me having a vehicle at my disposal is well worth paying a bit more for. For showers, most big truck stops you can buy a shower and do laundry on the cheap, and some will include it for free if you buy a certain amount of fuel.
When you're done with the trip, you could sell the RV and get some money back. If you're handy, there are lots of options of converting a cargo van on the cheap. You could also pull a small pop trailer if you have a car capable of towing, but they're not as convenient as get up and go.