The first time I went to Savannah, we stayed in a bed and breakfast by Forsythe Square. It was great -- but ridiculously expensive.
If you want to save a fair amount of money and you have a car, there are a bevy of decent motels on I-95, 15 minutes away from town. That's what we do now, and never have trouble finding parking in the city. Some of the motels have amenities that you won't necessarily find in town, like indoor pools, which is a great way to chill out at the end of the day.
Regarding site-seeing, stop at the visitor's center to see what's going on and to pick up discount coupons. I'd recommend an evening ghost tour, preferrably by horse and carriage if weather permits. The harbor cruise is dull, but if you're walking around all day -- Savannah is certainly pedestrian-friendly -- the boat is a good place to rest your feet. Paula Deen's restaurants aren't worth the wait or money. (Beware of tourist traps!) If you have it in you, climb to the top of the lighthouse in Tybee. As you can imagine, the view is great!