In terms of security, Recife is not at the highest level. It is quite easy to get into a bad situation here. In order to have a great vacation, you need to follow certain rules.
Taxis are the best way to get around the city instead of buses. When it gets dark, it's best to avoid long walks around the city, especially on Sundays. Leave all valuables in the hotel safe or don't bring them on vacation at all.
Don't forget the dangers of sharks. Look around for signs warning of danger before you enter the water.