Since you have 10 days, you can easily do everything multiple times. There's not a whole lot to do on Tybee Island, except the beach. There is the light house and museum. It's your typical light house, not the tallest that I've climbed, but still offers great views from the top. If you can get a complete tour of the museum, it is worth it. They may only do that for small groups, not sure.
There's enough to do in Savannah for a day or two. If you like trains, there is the Railroad Museum. There is also Old Fort Jackson. I'd recommend purchasing one of the trolley tours that will allow you to cover a lot of the city. There is ample parking on River Street, but I wouldn't take a RV into the city.
Fort Pulaski is about 20 minutes or so south and worth half a day or more. Skidaway Island State Park is a nice half day visit as well, if you are into hiking and nature. This is where I'd prefer to camp over River's End. Jekyll Island is about an hour south and is a very nice island. Only 35% developed where you can watch deer grazing in open fields, watch Alligators watch you and lots of other wildlife. The historic downtown district is a nice tour, the trolley tour is a little over priced as the area is easily walked.
Hilton Head is a short drive north from Savannah and worth a day's visit. If you don't mind road trips, I'd recommend heading north to Charleston if you've never been. We prefer Charleston over Savannah. For us, it is a 1 hour drive to Savannah and a 3 hour drive to Charleston. We'd pick Charleston every time and have done day trips to Charleston many times.
-Michael
