Bars
Soda
Soda can be pretty pricy in the hotels, and you will find it only on a soda tap if you are in a good restaurant; otherwise, you will usually get it in a can. The cheapest way to get this would be to go to a local "Food Mart."
"Goombay Punch" is the local soda. It has a pineapple flavor and is what the locals call a "Sweet" soda versus a cola. It is sold in cans at all grocery stores and also available in almost every Bahamian eatery.
Non-alcoholic malt beverages are also very popular. The primary brand of choice is Vita-Malt.
Beer
Kalik is the national brewery of the Bahamas and is always served at "all-inclusive" resorts. There are two rather distinct types: Kalik Light is a Budweiser-style very light lager, while plain Kalik has a bit more taste. Guinness is also very popular.
A new beer is available -- called Sands. It can be obtained at many resorts. It is a similar style product to Kalik.
Imported beer is can be incredibly expensive in the hotels but is not overly priced in bars and liquor stores. Cases of beer are readily available in a variety of Duty Free liquor stores.
In Freeport, the Port Lucaya Marketplace and Marina has many bars offering two Kaliks (and some other brews) for $5.
Hard Liquors
The Bahamas has significant amount of liquor stores in relation to the population of the country. You can find liquors stores downtown, by the hotels
Rum
This is by far the best choice of drinks in the Bahamas. It's as cheap as you can get ($2-$10 a bottle), tastes great, and it's made fresh by 3 different companies, the largest being the Bacardi Rum factory on New Providence south of Nassau, where you can take tours and get free drinks if you go on a 2-hour bus ride.