The difficulty is you are heading out in the coldest part of the year. The sections of the country that are feasible at that time are limited.

Testing your "go anywhere" statement. You could start out in NW Louisiana, head towards the Florida panhandle and then up to Washington. It's rather easy to avoid the interstates and you can find water every 10 or 15 miles. You can also avoid the big cities if you route carefully.

If it's possible to delay until March, it opens up a lot of possibilities.