Thanks for all the replies, everyone. You certainly gave me food for thought.
I've been researching this for a while, so for the benefit of future non-American readers, I can actually shed some light on the license issue.
As @maddog348 said, it's possible for a non-American to get a drivers license in some US states. As far as I know, the only difference is this would only be valid for one year and will need to be renewed. In Canada, it's possible to get a local license for 5 years at a time, for non-Canadians.
Clearly, we can drive with our Israeli licenses too, as they are international. We always take the extra step of issuing a formal international license on top of that, just in case. I do believe some states require that by law, though it's not a federal requirement and most states will accept a foreign license that meets the international standards (i.e. photo + name in English letters). Still, you never know what an insurance company will ask you for in case you make a claim so we prefer to be safe than sorry and spend the extra $5 on an international licence.
Of course, the issue here is with buying a vehicle, not just driving it. So, as far as I can tell, you don't have to be a driver in order to own a vehicle. Anyone can own a vehicle, they just can't drive it unless they have a license, right? As someone mentioned here, a company or LLC can own property, including a vehicle.
Since non-Americans can own property in the US, including real estate even, there's no real problem in getting a vehicle to your name. It's a hassle and you need a local address but it can even be the address of your hotel, the DMV doesn't really care. Clearly, you want an address where they can write to you, so most people give the address of a friend or relative in the US. The point is, the DMV doesn't care which address you give them and you don't have to be a US resident or citizen to register a vehicle to your name.
The main snag here - and the reason not many people do this - is the general hassle involved with buying and selling a vehicle. Just finding the right one usually takes some time. Let's say you're not pick and you just head out to the dealership, you'd still have to spend some time registering the vehicle. With a used car, you may need to run all kinds of emission inspections etc before you can get it registered. Not exactly a good way for most people to spend the first week of their vacation ;)
Even though we've had some very long road trips in the US, we were always trying to see and do stuff and preferred not to start (and end) our trips with the stress of buying and selling in a foreign country (it's stressful enough back home ;) ). Yes, renting is expensive, but it takes you 15 minutes to get the car and 5 minutes to return it and it's all by the airport. Plus, you're covered in case there's a problem. The rental company is supposed to replace your car or at least pay for anything that needs fixing if you happen to be in the middle of the Yukon (as we were last year - though fortunately, the car was perfectly ok).
So yeah, buying and selling is something I wouldn't get into unless I had to. Looks like it would be something we'd have to do eventually when we get our RV, I'm just not in a rush to do that in the first "test" trip where we'll just be getting a taste of RV life for a few weeks.
Again, thank you everyone for your answers. That was very helpful. Expect more questions from me in this forum because I have TONS of them :D It's so great to have so many kind people willing to help a newbie out - thank you!
