Beachy Budget Honeymoons in the United States?

My fiance and I are on a very small budget for our honeymoon. We are looking at a wedding in October 2014, so the honeymoon would probably be in late October.

We had previously looked into some Caribbean honeymoons, but our budget definitely doesn't allow those. Could you give me some ideas about places here in the States?

We are looking for something beach-y, romantic, relaxing, with some seclusion, ...and inexpensive.

Thanks so much for the help!!!