I went to Savannah a few months ago. I'll tell you this, beer prices drop about $1.00 for every block you move AWAY from River Street. You definitely want to wander down there and take in the atmosphere, but you won't want to stay long.
My other tip is if you have never had New Belgium Fat Tire or Dogfish Head 120 Min IPA, they are on tap EVERYWHERE in Savannah, and they are both great beers. I drank about 3 gallons of each the weekend I was there.
I wasn't particularly fond of Moon River. Nice place atmosphere-wise, but like noted before, right on River Street and $7-8 a beer for your typical standard (i.e., boring) IPA, Stout, Red, Brown, etc..
We had a great time at Wild Wing Cafe in the Savannah Market on Bernard St., which had about 25 beers on tap, though mostly mass domestics (I had about 35 Fat Tires). There is also a Wild Wing Cafe in Charleston at the end of Market Street that is smaller, but has live music most nights.
We also enjoyed the Rail Pub and Churchills in Savannah.
Both are great cities. Enjoy your trip!