DH and I just returned, and had dinner out each night. Right across the bridge from Disney is Shelter Cove Marina, and there are a number of restaurants in that complex.
We ate at Scott's Fish Market ... I had fried chicken dish, and would not recommend that. The chicken was soggy (not even closed to crispy fried), and it lacked flavor. However, DH had a salmon special they offered that night, and loved it!
Also ate at Little Venice, in the same complex. Both our meals were delicious. I had a pasta/seafood dish in a light tomato/basil sauce (don't remember the name of the entree). It had mussels, scallops (melted in my mouth) and shrimp. It came with clams as well, but I asked to hold them out. DH had spinach/ricotta filled raviolis, and they were delic as well! Dessert was good too - tiramasu and vanilla gelato.
On our final night, we ate at Captain Woody's in Palmetto Bay Marina (not Palmetto Dunes). It was recommended by the skipper of our Dolphin boat tour that afternoon as a place where all the locals go to hang out. We both had grouper - mine grilled and DH fried, and both dishes were fantastic!!
All 3 places had nice, casual atmospheres and appeared to be family friendly!
You'll want to talk to the cast members at the resort too ... Mike was one we talked to, and he said he's been there for 20 years I think, so I'm sure he'll have some great recommendations.
Have fun!!