You can check with your insurance company about a "vacation override" for travel. If your refills aren't due before you leave, your plan may allow for an early fill, but call them first for the details/restrictions.
Most (if not all) states do allow refill transfers from pharmacy to pharmacy. It does not have to be within the same chain, but if you use Walgreens/CVS/whoever, it is much easier. Some states do have restrictions (eg. NY only allows the transfer of 1 of the refills on a script at a time, and does not allow transfer of controlled substances). If its a new rx, you should be able to fill it at any state, though (again) controlled substances are regulated differently from state to state. Talk with your local pharmacist, let him know when you're leaving, where you're going, etc., and he should be able to assist you.
(Yes I am a pharmacist)