Book a trolly tour and be the there before they open...
Savannah Tours Voted #1 | Save Up To 23% On Savannah GA Tours
People don't seem to go early, you can ride the trollys all day long (getting on and off), and you learn a lot of information about the city from the drivers (be nice, bring a lot of 1's with you for a tip for the drivers who do keep you entertained along with information).
By trolly, you get "free" parking, you see the city at your pace, and free a ride back to your car. That said, when we visit, we usually come down for a day only from SC (about an hour north of Savanah), and if you're already staying in downtown Savanah, may not be worth the travel around town with free parking doing if by trolly if you're already there.
Savanah is a cool port town. Always love it when we're visiting. Lots of things to see and do. Touran trap for sure, but enjoyable for families, couples and singles.
I would highly suggest if you're looking at buying property, particularly within city limits, ensure you know all of the zoning and local town building ordinances. I could be wrong, but Savanah reminds me of Charleston SC, where it's a historical city and it seems like your buying into one great big HOA because those locations
WILL NOT lose thier "old charm" apeal to the tourists. So if you buy property, ensure you know exactly what you can do with that property before you buy it. Perhaps no different than living in Taxachusettes
PS, if you have a New England accent, lose it if you're buying directly from a local and not using a 3rd party buyer in Georgia (Florida who cares). It could save you at least 10%

(coming from a 20 year dam* Yankee to a Yankee)