Blue Crab Claws for the WIN!

http://www.waterman-galveston.com/

Fancy place, pricey, but darn good. Really upgraded since the old one was there. Used to be very few boats there...but now it's a full time marina on the weekend.

on the mainland at hwy 6 and Highland Bayou is Louis' bait camp. good food all around and maybe the best fried shrimp around. not on the island, but only about 10 min away.

If you are doing breakfast don't pass up the Gumbo Diner. Best breakfast I have found in Galveston especially their Beignet's.

Won't be much for the kids (they might have things outside to keep kids occupied), but if you're into beer stop by Galveston Island Brewing. They've started distributing locally so a lot of the local eateries have their brew, but they've got some good stuff on tap at the brewery.

Michael Burger is a lunch must. It's in Galveston too, which is what the OP asked about!
Michael Burger has weird hours, so call first to make sure they're open.

So far we've had Benno's and the Gumbo Diner. Benno's was so so... I just ordered the wrong thing. My wife's fried oysters were good, my fried softshell crab was not. Kids liked their fried shrimp. Gumbo Diner was really good. Crawfish etoufee was great. Shrimp and grits was also a must. Very pleased with everything. Will return there in the AM for beignets. I'll update later this week with further ventures.

go chase the sand crabs with flashlights! nightime fun with the kids

It is not a hole in the wall place but one of my favorites and one me and the wife hits each time before we leave is Millers. We were going there for breakfast a lot before we found the Gumbo Diner so we started going for lunch and dinner to Millers and they have always had great food.

Millers, Shycatz

Black Pearl Oyster and Gumbo Diner were our two favorite places. Overall winner was the Black Pearl Oyster for its awesome Black Pearl Po'boy. Overall, the only place I wasn't really happy with was Benno's, but I should have ordered something different. Now I'm back in Hallsville enjoying $1.50 tacos from the taco truck. Life is good.

Derek is a wise man. The place was great.

Actually the credit goes to DanDaBald. I only found it because I searched the forum before I went last year.

On The Road In Texas

Yep, Black Pearl Oyster bar is hard to beat!!! Plus they stay open later than a lot of the others. BPOB FTW!!!

Was gonna suggest Clary's as well, kinda upscale, but it was by far the best seafood on the island. However, after Mr. Clary died, it went down hill.

If your looking for a hole in the wall Italian place in Galveston, DiBella's is another hidden gem. The neighborhood is a little sketchy (31st street) but the food is top notch. They do have steaks and seafood as well.