I was there in early December and arrived by car a day early. My hotel was on Seawall Blvd., but it was too cold and windy to go to the beach; but in May that may be a perfect spot to visit. If you have a car, be sure to drive around the "historic" district and check out the wonderful Victorian-style homes, just east of downtown. Otherwise, don't expect too much. Also, while I would not normally plug any restruant, you must vist Saltgrass Steakhouse if you like steaks. Nothing fancy, but I had the best steak in years there. It's at the corner of Seawall and 15th Street.
Moody Gardens is delightful. We visited at Christmastime with my parents, who also live in Houston. There's an optional (extra-charge) butterfly "aviary" and a small but neat rainforest-type indoor garden, with animals native to some of the tropics (birds, lizards, and a serval, if I recall correctly). They also have an IMAX film there; the subject changes periodically.
Another very interesting thing to do in Galveston is touring an old oil rig platform. It's permanently docked near the cruise terminal as a museum, and has a lot of exhibits that explain the whole process of oil exploration and drilling. Whatever your personal feelings may be about the industry, it's guaranteed to be an education.
Galveston is a charming town. It reminded me a lot of New Orleans. When we went out of there(Feb.) they were celebrating their Mardi Gras as well. You can visit the sea wall. May will be a warm month. We walked around and visited shops and boutiques during our one day stay. Next to the terminal is a seafood restaurant. Casual dress, fresh seafood if you're interested.
If you have a car, then try out Nasa space center its very interesting about maybe 45mins to an hour drive north, In Galveston itself walk the strand very like new orleans without the crime, have a good texas size steak, portion size in texas is huge just like everything else here.
Kemah Boardwalk is very near by as well and a worth the time to visit. I agree with the earlier post about the Historical section, tours are available. Also the Strand for clubs and shopping, no rental car required.