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In general, Lagos has become a much safer place to visit than before, with the state spending huge budgets on security with police patrol cars, CCTV cameras. etc. But beware of deals or businesses that sound too good to be true especially e-mails soliciting your help, and do not openly flaunt your possessions, especially in public places.
While it is rare for a tourist to be a victim of a violent crime, it is still wise to stay safe and be alert, especially during late night outings. Stick to crowded streets and make sure to go out in groups as against going out alone.
Lagosians are generally nice and friendly people, most of whom will readily offer directions to you if you are lost.
Lagos still has its fair share of odd people: street beggarsboth the old and young, people with psychological disorders, etc. If someone approaches you for money, do what most Lagosians do: completely ignore them or continuing to walk at a brisk pace.
There are a few police officers who are corrupt and inefficient so it is best that you stick to the law and avoid going anywhere off the beaten path without a trusted guide, especially if it is a first visit.