I just returned from a trip to Sanibel Island and did some research on this board so I thought I would report back on the places I tried. I was with my 5 year old daughter.
Schnapper's Red Hots was fun and tasty. We had grouper sandwiches, fries and a vanilla shake. Fresh, good fast food. There is only a small, rather grim outdoor seating area but you are in and out quickly so it doesn't really matter.
The Island Cow. A very kid friendly place and my daughter liked her shrimp basket. But I would not go back to this place. Also the portions were insanely huge.
Traditions on the Beach was our hotel restaurant at the Island Inn and it was over-priced and not very good. Pastas were over-cooked. The clam chowder was good. I would not return there. By the way no-one on this board recommended it :) We loved the Island Inn though, a wonderful place to stay and very quiet.
Over Easy Cafe was a highly recommended breakfast spot but I thought it was just average. My banana pancakes tasted like they were made from a mix and they didn't have real maple syrup. Very good freshly squeezed orange juice and friendly service though.
Sweet Melissa's Cafe. This place was very good and in fact we ate dinner there twice. Everything was well prepared and delicious. Although it is an upscale place and not geared towards kids, they were extremely friendly when I walked in with my daughter and they were willing to add shrimp to their kid's menu pasta for her.
My tilefish with rice, peas and mint was excellent. Obviously this is not a budget option but it was worth splurging on. Highly recommended.
Thanks for the recommendations everyone! Although the food was hit or miss, the people everywhere we went were incredibly friendly. We loved Sanibel and hope to return some day.