The only place we ever stayed in Savannah was the East Bay Inn. I can highly recommend East Bay due to its location, affordability and Southern Hospitality.
Whatever place you decide to stay, take the following into consideration.
1. Make sure if you are renting a car or driving that the hotel has parking and factor in if they charge you additional to park.
2. Stay downtown, the hotels further out are a little cheaper but by the time you factor in the hassle of finding and paying for parking it really is not worth it. Savannah is very much a walking city and with the "To Go Cups" you really want to be able to just walk back to your hotel.
3. Think about the location based on what you want to do. The hotels on Bay /River/Broughton street are really nice but it can be a very populated high energy area. If you want a quite restful experience then pick one of the B&B's a few blocks west of the river.