Nina,
First of all I moved your posting from the Dashboarding Forum since this board is more active and more likely to give you responses.
The bigger problem being 17 is not from hotels but from the border crossing. Generally motels are not going to ask for your age unless you look "too" young.

If you visit east coast schools and still want to visit the Grand Canyon and California, you will easily drive over 7,000 miles. How long is your planned trip? How much $$ are you planning to spend?

Editor