Drinks are available all over Abuja and are very overpriced. You have the choice of local drinking joints or fancy spots. Average $20 US for some mixed drinks. 5-9 dollars for a local beer. Buy beer from the Market and you will save a lot of money.
The major hotels have bars and restaurants - watch out for the prostitutes, if you ignore them, they get really offended. If you are not interested, just say so and have a short conversation, then they will leave you alone.
Ceddi Plaza Has a bar on the basement level.
Blakes Has live music or a DJ and drinks as well as the fish bar
British Village Requires a membership to enter and is popular during different sporting events, especially during soccer games and rugby.
Tucano's is in Asokoro - a night club
Orchard Garden. Local outdoor place near Millenium Park, set in a grove. Beer around 250N, small BBQ serving e.g. whole grilled fish for 2000N.