It will be by far difficult to pay with US dollars. Exchange cash in local money and always bring small bills with you. As they often refuse to give change.
In Abuja there are many cafés serving local cuisine for very low prices. Try to eat out where there are lines of local people. As to the water, drink only bottled one. Especially don’t buy water sealed in package.
Making an order in a café, keep in mind that they use the word “soup” for a dish which looks more like a heavy source than a liquid dish generally served in other countries.
If you arrive at night, wait till morning for the safety reasons. Then you can continue your way wherever you would like to go to. Generally speaking, don’t go out after dark at all in Nigeria.