Ghost tour we did was fun. Totally agree on the squares, historic home tours are nice too. Mercer house is open now and is a good choice. Juliet Gordon Low house is another. Agree that River street is just tourist trap stuff. City market has gotten a lot nicer though. The on-off bus is honestly a decent way to get around on your first day, and get a feel for where things are. Hopefully your AirBnB is in a good spot.
I never much focused on the food, because we always go back to the Beaufort area and there is tons of low country cooking to be had there. Best shrimp anywhere down there. Don't eat at the Pirate House. Moon River brewing is just ok. Savannah is one of the few places I've seen outside of NOLA where they have the slushy booze drinks on the wall (it's a disgrace to the original Hemingway Daiquiri to call them Daiquiris).
Always fun to re-watch
Midnight in the Garden of Good and Evil before you go...or read it if you haven't. I picked it up in the Savannah airport long before it was a best seller and movie. Solid read.
Edit: meant to tag
@Guapo