Just north of the Florida - Georgia border is the wonderful town of Brunswick. It is the site of the Federal Law Enforcement Training Center (FLETC), there is a small airport serviced by Delta out of Atlanta and there is an abundance of places to stay including a Marriott property. The reason I recommend this area is the natural beauty that can be found in the surrounding areas including a state park called Jekyll Island. This isn't a destination for someone looking for amusement parks or theaters but its a fantastic place to relax and enjoy southern hospitality.
There are some sites that must be seen such as the Lover's Oak and the Marshes of Glynn. Both are easily accessible.