Abuja is a sprawling planned city, and walking between sights is not realistic except within individual districts. The main options are taxis, ride-hailing apps, and occasional minibuses.
Ride-hailing. Uber and Bolt both operate in Abuja and are generally the most reliable and cheapest option for point-to-point travel. Wait times are short in Maitama, Wuse, and the Central District; longer in the outer areas. Having a working Nigerian SIM card helps considerably.
Taxis. Yellow taxis circulate throughout the city. Negotiate the price before getting in — meters are essentially unused. Rates are generally reasonable but will always open higher for obvious foreigners.
BRT and minibuses. A Bus Rapid Transit system operates along the main corridors and is cheap but slow and not well suited to tourist itineraries. The route from the Central District through Wuse to Maitama is the most useful.
Car rental. Available from the airport and most large hotels, typically with a driver. If you're heading out to Zuma Rock or elsewhere in the region, this is the most practical option.