Pretty much each of the above mentioned comments are applicable to Savannah probably the two best choices would be the hotel option or if you have to you can park at the chamber of commerce which resembles an old train station it's where all of the paid trolley start. Honestly the trolley tours aren't a bad deal very reasonably priced you can ride around with a guided tourist you can hop off see something get back on really a great deal I would recommend that first that way you can see all of Savannah with a guide or you can hop off and hop back on it anytime and at the end of the tour you're back in the parking lot with your vehicle
Walmart. Churches. Truck stops. Hospitals. Etc. Almost all of them (everywhere in the US) will allow you to park for free over night for free. Even sleep in your car if you want. Started parking lots are a little more tricky, but usually work.
Sunday is free parking everywhere. Not sure if there's any free parking during the week.
you can valet park at the hotel and take the tour buses.
Thanks! Your answer is awaiting moderation.