Galveston doesn't have any professional sports, unless you head north about 55 miles. So what's left for the sports fan? How about some high school sports. Ball High can be fun during football and basketball season. There are some heated rivalries (i.e. La Marque) that offer a good show for a cheap price ($1-2). If you don't mind sitting with some rowdy high schoolers, go for it, it's a lot of fun.
Bottom Line: There's nothing quite like watching hungry high school football players giving it all they've got to win a rivalry.