I lived down in SW FL late 80s to early 90s, and was a recruiter in both Ft Myers (no additional "E" in it) and Naples from 03-06 and lived in Lehigh Acres then, I left when my recruiting tour ended, and when I couldn't find anyone at WalMart that spoke English I knew it was time to move back west. My info on the area is dated, definitely when it comes to home values, so grain of salt, YMMV, yada yada...
I completely agree with the recommendation of Bonita Springs as the best bang for the buck in that area. Ft. Myers, short of San Marco area on the south side, is straight up gang territory and isn't near the beach anyhow so I'd recommend nixing that right off the bat. FTM Beach area has a great pier and a good beach, but prices there will likely be out of your stated range. Same goes for Sanibel for sure, and add Marco to that. Last I was there, a run down 1200 Sq/ft home on .1 AC in either Sanibel or Marco ran in the $600s and up. Granted, that was before the housing bust and I would still look, but prices there are outrageous. The Cape Coral that I knew was high for property crime, typical punk type shit, and had some real shitty city ordnances that I disliked as well as the toll bridge racks up quick, again not on the beach either.
But Bonita and Naples, both great areas with low-ish crime (still too high for my present likings), good beach, Naples at least had a good pier but no idea what the recent hurricanes did to it. Avoid Golden Gate, it was getting pretty bad with MS 13 when I was last recruiting there, lots of illegals moved in with 20+ member families buying homes in the 00s. The closer to the coast you get, the prices go up and the crime goes down, I'd recommend you buy the most you can afford if you want the best neighborhood possible in that area.
Me personally, I was more partial to the Melbourne area on the east coast, better fishing in Mosquito Lagoon than FTM Bay, quieter over there, and you get to watch every launch if that's your thing.
But me personally, I haven't missed Florida for a second since I left there 13 years ago.