The good news is that internal flights are incredibly cheap. Domestic flights do not leave from Murtala Mohammed airport but from the older airport 10km away. Private airlines are a viable alternative and are usually more organised and reliable than Nigerian Airways and offer relatively cheap fares. Travelling by bus is the safest and most comfortable way to travel and lines connect all the main cities. Bus offices tend to cluster in the same area of the city.
Nigerian drivers have little respect for speed limits and accidents are often fatal.
There are trains running in Nigeria but they're not very comfortable and, as if to compensate for the bush taxis, travel at a snail's pace. We encourage you to verify any critical information with the relevant authorities before you travel. This includes information on visa requirements, health and safety, customs, and transportation.