I get the feeling that the speaker was on the road far from home and was having a horrible time, for whatever reason. He meets a girl at his lowest point and she brings him out of that low point. He realizes he loves her and wants to go somewhere that they can be together without any interruption, so they go off to Savannah (which is in South Carolina and Georgia, but SC is where the band is from) to be alone and start over.
I get the feeling that the speaker was on the road far from home and was having a horrible time, for whatever reason. He meets a girl at his lowest point and she brings him out of that low point. He realizes he loves her and wants to go somewhere that they can be together without any interruption, so they go off to Savannah (which is in South Carolina and Georgia, but SC is where the band is from) to be alone and start over.