Nigeria is one of the places where Guinness is brewed outside of Ireland. And they do it pretty well, although it's not the same product. The Guinness brand with logo and copyrights where they should be is also used to brew both an alcohol-free malt version of the black stuff, and an extra strong about 7.5% version of Guinness in Kenya in the case of the latter and Tanzania in the case of the former.
Beer is actually big business in Nigeria, although the move toward evangelism and Islamic law is making its mark. Lagos is relatively unaffected due to its cosmopolitan nature. Heineken, Star, Harp, Gulder and other international beers are available.
Malt beverages non alcoholic are very common in Nigeria.
The other cheap drink of choice is gin, which is locally made. Some locals will swear to it making their step uncle's dog blind, though, so be careful.
Never drink the water sold in plastic bags, except they have a NAFDAC registration number on them. It probably hasn't been boiled, and may carry some nasty diseases. The bottled water and other soft drinks are safe.
Other drinks to consider include: palm wine, wine, zobo red soft drink, is a tea of dried roselle flowers, kunun, kai kai also called ogogoro.
The northern states have implemented Sharia Islamic law, which means that alcohol is prohibited. Ironically, the only places where you can drink a beer in these states are the police staff bars and the army barracks, because these are institutions under federal law. Beer is available in Kano, in restaurants managed by foreign or Christian people, Chinese restaurants, and/or French cafes.
For a real night out, go to the Sabongari area of the old town. Plenty of bars around that stay open till very late. Many do decent food as well. Sabongari is also the place to buy alcoholic drinks and there are plenty stores open late into the night. Some hotels in Kano are "dry", however in Tahir Guest Palace the staff will be quite happy to buy you a few bottles of beer for you in your room all rooms have large fridges.