Absolutely! Just for sake of reference, River Street actually fronts the Savannah River while Bay Street is the next one up.
Places I highly recommend all on River Street are:
The Cotton Exchange Tavern - awesome clam or crab chowder, grouper fingers, various sandwiches. Sit at the bar for a great time with the bartenders and meeting other visitors! If you're there during the day at the bar, ask for Jean and tell her Rick & Belinda say hi!
Huey's - love their Cajun breakfast menu and Bloody Mary's!
Tubby's - upstairs from Huey's for a great outdoor deck overlooking the river, usually has live music outside.
Rock's On the River - atop the Bohemian Hotel for drinks and sitting out on the open air rooftop looking down along the river!
River House Seafood Restaurant - very good menu with some great true seafood dishes. you can usually sit outside at sidewalk tables if weather permits.
Vic's On the River - for more elegant dining yet a relaxed atmosphere, i.e. you can go there without having to get "dressed up". Usually has a piano player.

Off of River Street:

The Old Pink House - splurge and have dinner in this beautiful old antebellum mansion on Abercorn just a 1/2 block off Bay Street!! Fun jazz bar in the basement!

B. Matthews - for a unique breakfast/lunch menu in a nautical setting. Also on Bay Street.

City Market - just a few blocks in from the river full of various shops, restaurants, and usually a live band outside on the weekends.

BTW if you're there for the 1st Friday of any month they always have fireworks over the river that night!

That should give you enough to do. <img src="http://www.traveltalkonline.com/forums/images/graemlins/Grin.gif" alt="" /> We're going back to stay at our favorite place The River Street Inn this December and can't wait! <img src="http://www.traveltalkonline.com/forums/images/graemlins/dine.gif" alt="" /> <img src="http://www.traveltalkonline.com/forums/images/graemlins/Clapping.gif" alt="" />