For restaurants, it's all about what you want. I imagine since you're going to the island you want some seafood. If you want a great plate of food at a reasonable price ($10-$18 a plate) go to Casey's Seafood Cafe on Seawall and 37th st. They use the same kitchen as Gaidos (the best and most historic restarant on the island) but they are much more casual (jeans and tshirts OK). If you want to really go all out, then go to Gaidos, but dress nice and be ready to spend ($20-$40 per plate) but it's worth it, it's been open since early 1900 and there is a reason why.
If you are in for some american food (burger, fries, etc) you can't beat The Spot on Seawall near 31st st.
If you want some mexican, I highly recomend the fajitas at Salsa's Mexican Cantina on Seawall and 46th st. Also, for a quieter mexican environment and wonderful platters, The Original Mexican Restaurant is on 14th and Market street back by UTMB, near the Strand.
Things to do:
Tour Ashton Villa (oldest mansion on the island) on Broadway
Tour the Moody mansion (home to the most powerful family ever to reside on the island) on Broadway
Tour the Bishops Palace near the old Catholic Church (We're proud of our old mansions as you can tell)
Go to Moody Gardens and watch the 3D Imax, or tour the Rainforest Pyramid, or the Aquarium Pyramid (89th st and Jones Rd on the Bay side of the island)
Go to Schlitterbahn Galveston (next to Moody Gardens)
Go ride the Ferry to Boliver Peninsula and back
Ride bikes up and down the seawall
etc
etc
etc
Galveston AttractionsWhere to shop (Galveston has tons of unique shops)Outdoor FunNightlifeWhere to eat*I don't work for the chamber of commerce, but after reading this post, they should hire me!