I agree with GLC, I really think your best bet will far and away be to keep one of the cars you already have and sell it in Vancouver at the end of your trip.

Selling it in the US will generally not be possible - at least not in a practical sense. Importing a car for the purpose of selling it (which is what you'll be doing since you aren't planning to move here) is going to flag all sorts of red tape from customs - which will involve fees, taxes, etc. Not to mention, a Canadian car with its Metric Speedometer/Oddometer is going to fetch a significantly lower price in the US.

You generally need a state drivers license to register and insure a car. Having a brothers address will only be of limited help because, a- he lives in Georgia and you're looking at buying a car in the New York area, and b- you typically have to provide some sort of proof that you are actually living at that address by providing a utility bill, a lease, or some other proof (which may not be possible since you are visiting as a foreign tourist).

When you factor in all of those things, plus the likely un-reliability of a $2000 car, especially one you don't know the history of, I just think your life will be a whole lot more simple and you'll be able to spend much more time focusing on your actual trip if you just go with a car you already have.
is it safe to keep expensive laptops, cameras etc. in a motel room? If not there, then where?
I've never had a problem, but if you are concerned almost every motel will offer a safe - either in the room or behind the front desk.