I cycled the Brazilian coast starting in Fortaleza several years ago. Ceara is a wonderful place, I was fascinated by the landscapes and small towns of the sertão, the semi arid geographical region just a little inland from the coast, and I really enjoyed the week or so I spent in Fortaleza (despite the fact that this coincided with a tropical deluge.)
The murder and crime rates in Brazil are spectacular but warrant a caveat - a more detailed inspection will reveal that the violence is concentrated in the favelas of the big cities and to lawless frontier towns in the interior where minerals or dodgy land acquisitions draw many trying to get rich quick. In Rio and Sao Paulo gang crime can spill over into established neighbourhoods thus resulting in the international headlines but the vast majority of victims are from the favelas simply because of opportunism and vulnerability. Recife consistently has a much higher homicide rate than the two more infamous cities to the south but gets almost no headlines as the violence is almost entirely contained to the poor of the favelas and rarely interferes with anyone's vacation. I rode through Recife completely unaware of this statistic and didn’t feel the slightest bit intimidated. In fact the only time I felt worried at all was when cycling through favelas on the outskirts of Salvador, Sao Paulo and Rio - I can't say I really felt unsafe once inside the cities themselves.
Most of the homicide victims are killed in gang violence or by police when the turf wars escalate to a point that they can no longer ignore the lawlessness and go in guns a blazing. In recent years the murder rates of the big cities have actually declined and are lower than some US cities - its only when the statistics are isolated to certain neighbourhoods that they are up there with South African, Colombian or Russian cities. The declines are being put down to better policing (ie they aren't killing as many people indiscriminately), earlier closure of bars, and a cessation of some long running turf wars which had contributed to large proportions of the homicides.
Fortaleza and Natal, however, are completely different propositions to what has been spoken about above and while the locals will warn you about the favelas they are nothing like those in the cities previously mentioned in terms of gang crime, gun ownership, drug saturation or police brutality. This was about 5 years ago and the situation may be changing slowly due to increasing wealth disparities and more disenfranchised migrants form the sertão, but don't let this put you off, Fortaleza and Natal are worlds away from the violent image of Brazilian cities perpetuated in the media. I would thoroughly recommend at least a visit - its a fantastic part of the world and the people are beautiful.
PS - If you would like any info on lesser known places along the coast in the north east, PM me.