No, no, no to the hitchhiking. That can be a very dangerous thing to do in the US (giving OR taking rides). If you want take it very slow and don't want to drive yourself, you could always take the Greyhound bus. I will still recommend driving though if you can.

Fun things to do in GA:

Savannah is quite nice and good for a stop if you can.

Providence Canyon in west central GA is wonderful -also called "the Little Grand Canyon" - I think that it is a kaolin area

We enjoy tubing down the Chattahoochee River in Helen, GA at Cool River Tubing - you sit a a giant blow up innertube and float for a few hours down the river - you can probably skip the town itself though - it reinvented itself as an "alpine village" twenty years ago or so and is quite touristy

The N. GA mountains and Stone Mountain just to the east of Atlanta are nice for a hike

Have a great trip!