Wilma,
I don't know exactly what you're looking for, but it sounds like you want more of a special occasion type restaurant for your anniversary and from what I can see, Galveston may not have a lot of great choices for you there, as most of their restaurants look like steakhouses, Mexican food cantinas or low end seafood shanties. It seems that the best fine dining restaurant is located at the
Moody Gardens Hotel and Spa on the ninth floor, but then it isn't rated very well online on TripAdvisor or other sites.
What I did find is a
fabulous place that sounds like just the spot you're looking for. It is called Charivari Restaurant and it is located in Houston, just about an hour down (or up) the road. It is known for its distinctive European cuisine prepared by its chef and owner Johann Schuster who was born in Transylvania. What grabbed my eye about them [as relates to you] is that they were just voted the
Best Anniversary Restaurant for 2008 by Citysearch.com.
So, I know that this may not meet your needs exactly, but it could be great if you can rent a car while you're there or even have a limo drive you back and forth if you have the money. Heck you might even decide that you want to be in Houston instead. If you do, we have some other recommendations for you in terms of romantic boutique hotels in Houston.
FT