Meh out of all of them I would say Mosquito. But I would check out 901 postoffice. That is the name of the restaurant. Galveston has a lot of really good places but barely any great places IMO. We always enjoy Galveston for the little hole in the walls. For that we go to Gino's at the corner of 61st and Stuart. It's Italian. I would get pizza or stromboli. I love the eggplant parm as well. They also will deliver anywhere on the island. If you happen to have a beach front hotel... that can be very nice. :)
901 was one of those situations where there were two people involved, let's just say it was best they are now separate. It was Galveston's gain as The Porch Cafe is a great new addition to the island with a unique style, location etc. along with fantastic food.
In any Galveston list I think Rudy & Paco should also be included with one note, they are about the only island restaurant with an actual dress code so be aware.
I also would recommend Olympia Grill on the Pier at Harborside if you like Greek food. The restaurant is very nice, has a great outside dining area over looking the harbor and some very good food.