I'll suggest Parrot Key at Salty Sam's Marina. Excellent food, wide age group (a place for families and people on dates, not particularly a singles place), entertainment most nights and a very tropical venue that is a lot of fun. Those "locals" that say its' a tourist trap are missing out on about the only good consistent restaurant in the Fort Myers Beach area.
I've had some great meals here. Saturday nights are a hoot with an entertainer that does imitations and at times you will see grandfathers dancing with their tiny grand daughters, older couples dancing and a conga line. Not a sophisticated venue, but you did ask for a family restaurant. LMF