The Orange Hill is a quiet budget hotel across from a quiet beach and convenient to the airport, offering a low-cost, Family Islands–type stay on big, bad New Providence.

This is a laid-back place. The bar is on the honor system (just grab something from the fridge and jot down your room number). The food at the dinner buffet is very tasty (though closed Wednesdays and Saturdays). 
Yes, the basic rooms of pine furnishings and tiled floors are rather dated and worn—though comfortable enough, and with sea views from the balcony or patio—and yes this hotel is a bit out of the way—though that can be a good thing, if you do not want the resort scene or downtown bustle. But you can always hop the jitney (bus) into town, and taxis are plentiful, if not cheap. 
The poolside rooms come with three beds (good for families), while the studios, apartments, and cottage all have kitchenettes.