I grew up about 30 minutes north of the island and have spent summers and weekends and random evenings down there my whole life. So here is my two cents worth (and they are just my opinions):
Hotels:
I am not really impressed with too much down there as far as hotels go. You don't really get what you pay for and you can end up paying alot. Most of the hotels are very dated. Escape! is newer and I don't know a thing about it....it may be one of the better places down there. I recently went to a wedding at the Galvez and we stayed there on our wedding night and had the sunday brunch there (awesome!). The common areas are beautiful and very reminecent of Galveston's hayday. The rooms are small and dated and NOT at all what you would be expecting for the prices. We also stayed at Moody Gardens hotel a year ago and aside from the convenience to the attractions there and Schlitterbahn, I can't think of anything to recomend it. I have heard decent things about the San Luis but again, not going to justify the price. The FlagShip (now named something else) is AWFUL, the Tremont is very "historic" (old). I hate to be a downer about the hotels but I am very picky about where I stay and if I had to stay at any of these....I guess I would go for the San Luis. Or I would rent a beach house or condo on Galveston or Tiki Island. Then again, you may be on the right track with Escape!
Restaurants:
We love Willie G's and Gaido's the best. Mario's is also very good (both locations)as is the Mosquito Cafe and the Original Mexican Cafe. DiBella's is pretty good and I hear good things about Rudy and Paco's and M & M Palms (expensive). A great place for a burger or a po' boy is The Spot. The Rainforest Cafe is right there by the San Luis and it is a really fun place for the kids. There is a volcano and a water ride inside the restaurant. The food is average/good but its more about the atmosphere for the kids there. There is a web site called b4ueat dot com that will give you restaurant reviews for the entire Houston and surrounding areas.....it's great.
Things to Do: (beside the beach)
The Strand has lots of shops. Tacky souvineers, nice boutiques, island wear, etc. There is also a place called the Peanut Butter Wearhouse that is basically a huge rummage sale but they do have some very intersting, if not valuable, antiques in there. La King's is an old time soda fountain/candy store that you cannot miss. There are also some great used book stores right off the Strand that I have found some real treasures in! Don't miss the Strand.
Moody Mansion and Ashton Villa are some pretty neat tours if you are into that sort of thing. The Library there is also very historic. Also, depending on when you go, they have the Galveston Historic Homes Tour and that is very interesting if you love history.
Moody Gardens has some great attractions and you can check all that out on their website. Next door to that is Schlitterbahn. I grew up going to the original park in New Braunfels every summer and everyone I know that visited the original park hates the new one. Everyone that I know that has been without that point of reference said it was ok. I have never been so I can't judge but I did stay next door with a window facing it and to me, it looked really small for the amount of people they had crammed in there. Maybe on the off season it is not as bad.....you might look at Palm Beach at Moody Gardens as an alternative if you are not looking for thrill rides.
There is a great film about the Great Storm of 1900 that plays at the theater at Pier 21 (which is right next to Willie G's).
There are also some great local bands that play down there at places like Yaga's, The Old Quarter Acoustic Cafe, 21.....and the San Luis just opened a new pool side louge called H2O that sounds pretty fun. Plus there are alot of other bars down there. There used to be a place that had karaoke on the Strand but since I know it has changed hands, I don't know if they still do that but there is another place that might, you would have to look into it.
On the seawall you can rent roller blades, those bike things that sit two people in front and two in back, and stuff like that. And there are alot of surf shops on the seawall as well.
Like a PP said, do not go down there on Kappa weekend if you can help it. The Island is packed, the college kids get CRAZY and it is really hard to get around. The police also get really tense and short tempered having to control the crowds and the hotel situations. I am sure it is a blast if you actually went for the party but if that is not your reason for going, I would pick a different weekend.
I LOVE Galveston!! Beach-wize, it's not Destin or even Gulf Shores but there is alot to do and it has a wonderful history. I could go on and on but I will stop here. Hope you have a wonderful time!!!