I haven't read all 8 pages of comments, so I apologize if what I write has already been said. I've lived in SW Florida since 1994 and, although crime is on the rise, I feel safe living here.
When I lived on Sanibel Island I only had to worry about running into an alligator.

Fort Myers has a lot of crime like any city, but it's concentrated in certain areas or pockets. Still, it isn't a place where I'd walk around late at night by myself (and I'm from Boston!) There is a lot of crime near the downtown area and some people have been attacked at the mall, although they've beefed up security quite a bit. Common sense should tell you never to walk to your car alone at night wherever you live.
I've lived in Bonita live near the beach for years and, although I haven't seen a lot of crime, my home was burglarized once, but that's it! Of course, after that I didn't have anything to steal.

Also, I don't have a garage and my car alarm has been set off once or twice at night. One night I ran out (which was a stupid reaction) and saw someone take off in a car. The next morning I noticed there were scratches around my gas tank, which is puzzling since it's locked. I'm not sure if they can be pried open. I always take my cell phone and GPS out of the car. I mean, who would even think of worrying about a gas tank of all things?
I was also surprised by the statistics I've seen on crime in Fort Myers. I worked in South Fort Myers for several years and never had any trouble. Bonita Springs also has a bad rating, so I don't know what they're using to get to these numbers. Supposedly, they're based on the police reports filed it these towns.
Someone wrote that the police here do a great job. That hasn't been my experience, but I won't elaborate except to say they don't seem to care, that is, unless you're rich. Maybe they're just too busy handling gang violence in the other parts of Lee County and have to prioritize.
My suggestion is to check out the Crime Beat section in the Fort Myers News-Press on a regular basis. Also, the sheriff's office might have a crime map that shows the various crimes committed and the neighborhoods with the highest incidents.
Keep in mind that Florida is very diverse. In one neighborhood you might have a mix of old shacks, trailers and million dollar homes. Someone here mentioned $150,000 houses. I haven't seen any single family homes in Bonita Springs or Naples for that price. In parts of Bonita or Naples Park you might find a small older home for under $200,000 but the same money will get you a brand new $1,800 s.f. house on the Cape or in Lehigh, although they're very different cities.
To people who have never lived in Florida, one thing I learned about is "deed restrictions." Some people don't care for them, and I never thought I'd want to be told what I can or can't do with my own property, but I now welcome some rules. I mean, who wants to buy a nice home and have next door neighbors who park cars on the lawn or raise chickens?
Good luck!