If you have flexibility of when you go, it would be a good idea to try and pick a weekend with smoother seas forecast especially if your son is not hooked on offshore fishing. If it is then or wait for months then I would go anyway and select a boat with catamaran hull because they are MUCH smoother riding. My first choice would be the outfit on the following link because I am familiar with them and have had good experiences. Located in Port Aransas.
http://wharfcat.com/Other catamarans that I do not have experience with in Galveston
http://www.galvestonpartyboatsinc.com/http://www.galvestonfishingboats.com/I also recommend sea sick medication in advance of the trip with rough or smooth seas. If you can choose a weekend with nice seas then there are a couple more outfits to choose from, but even then a catamaran hull is smoother and might be the right choice until you know if or how much he struggles with sea sickness.