Native Savannahian here. Grew up there, left for 14 years, and came back 25 years ago.
I'm a fan of the Gastonian and the Kehoe House, as far as B&B's go. The Perry Lane, the Andaz (on City Market) and the Mansion on Forsyth Park are my favorite hotels. The Hyatt is centrally located downtown, but as far as I'm concerned, it's just another Hyatt (seen one, seen them all).
As far as restaurants go, I love the Pink House (historic; George Washington had a drink in the basement bar once. Get the she crab soup), Vic's on the River (where you can see a map drawn on one wall by Sherman's officers when they occupied the city in 1864; try the fried green tomatoes, and they have a truly outsanding meat loaf), Elizabeth's on 37th, Alligator Soul, Local 1110 (near Forsyth Park), The Vault, Cotton and Rye, the new Husk restaurant (sister to the one in Charleston), The Grey, and Treylor Park. For burgers, look at the Green Truck Pub and the Crystal Beer Parlor. Spanky's on River street has great pizza, as does Vinnie Van Gogo's in City Market. And for sandwiches, I'd go to Zunzi's, with South African-themed selections that are to die for. It was recently rated as the best sandwich place in Georgia. Get the Conquistodor. It's like nothing you've ever had anywhere.
These are all downtown. There are good places to eat elsewhere (Tybee, Southside), but there are so many good places in the historic district within walking distance that you really don't need to venture outside the downtown area.
