Recommended by the locals and away from the tourists is Mosquito Cafe in Galveston!
The restaurant is in the East End of the Historical District in a resorted 1870 building.
At Mosquito Cafe, they have fresh, homemade food and a lot of gluten free options. You order at the counter, select a table and the food comes to you.
Our chicken sandwich, veggie burger and kids meals came pretty quickly and was very good. My kids even commented on how fresh the vegetables were.
The only thing to know is that it gets crowded and for big families, you might want to call to reserve a table at peak times.
And while you are in Galveston, find lots of things to do with kids, HERE!