There are some decent public schools in the area, but you should definitely check the zones when purchasing, because there are few different zones within Lee County and even though School Choice allows you to choose a school, you must stay within the zones.
I have an 8 year old boy and a 6 year old daughter, and I did move my 8 year old to Canterbury (Private) this year because I was not happy with the choices offered in my zone.
If private schools are out of reach, I would suggest for you to take a look at the following site: http://www.greatschools.org/florida/fort-myers/Lee-County-Pu
There are reviews and ratings, very helpful to see what other parents have to say...
As far as elementary schools, I've done extensive research and believe the only one worth trying to get into is Allen Park Elementary :
All the rest are not bad, but not great either.
If you like to chat more, drop me a line in my e-mail and I promise I won't sell you a house, since I don't sell homes I'll just talk to you regarding schools ;)