I lived in Savannah from '72 to '73 and then again from '82 to '88. River Street along the Savannah River is the heart of the historic area because that is where most of the bars and restaurants are located and it's fairly safe. They were 3 story tall cotton warehouses and now the bottom floor is the bar or restaurant and the top floor faces the other way on Bay Street and they usually rent them to offices and shops. I haven't stayed at the Hyatt, but I've been inside and it's pretty neat. The Hyatt Regency is the big hotel that actually sticks over River Street, here's a photo looking up River Street. From that hotel you can walk to most of the places on that street. I think it's on the very expensive side.
See those railroad tracks, my first job after I got out of the Army was as a switchman with Southern Railroad. We would bring sugar trains down those tracks to the sugar refinery and often we would spend a lot of time looking for the owners of the cars parked on the tracks. They have since built parking lots and all that bad parking went away.
St. Patrick's Day is a mad house, it's the biggest celebration outside of NYC. That street will be packed with 300,000 all drinking green beer and a huge parade. I only went once. The Hilton Hotel is also nice, but it's a few blocks away and you'll to drive to most things.
There's an island in the middle of the Savannah River, which separates Georgia and South Carolina. About twenty years ago they built a resort there with a golf course. You can probably reach downtown from there over the bridge in a few minutes and yet you would be away from the hustle and bustle of the city. It's called the Club at Savannah Harbor, you can see across the river and that's River Street.