Abuja is light on traditional tourist sights — it's a planned city, not an ancient one. The main draws are the dramatic landscape, a handful of cultural institutions, and easy access to Zuma Rock outside the city. Eagle Square, the national ceremonial ground, is worth a look if you're nearby, and the Nigerian National Mosque and National Christian Centre together make a good half-morning tour of the Central District.
The Aso Rock monolith looms over the Presidential Villa and is the defining feature of Abuja's skyline. You can't access it directly, but it's hard to avoid. For a more grounded experience of the city, head to Wuse Market — the busiest market in the capital and the place to eat proper Nigerian food.
The Millennium Tower project in the Central District is an ongoing curiosity — a grand prestige building that has been under construction for years with no clear end date. The Abuja Arts and Culture Centre has rotating exhibitions of Nigerian art when it's open. Maitama is the diplomatic district, pleasant for an evening meal if your budget allows.