Convention Centers create income for the city, a city which, if I believe the hype, is suffering from a drop-off in tourism.
Tampa built a convention center and it stays booked up solid. In fact, the city is looking to expand it so that it can bring in more business. The Convention Center is the cornerstone of a plan the city has to re-do the downtown warehouse sector, with the Florida Aquarium and the Ice Palace/St. Pete Times Forum anchoring the other corners.
We also used tax dollars to build the new Bucs stadium, which does pretty steady bookings with stuff other than Bucs football games (Outback Bowl and USF Bulls come to mind). The stadium parking lot is also used for small circuses and the county fair. Of course, in my opinion, the Glazer Family pushed to have a perfectly good stadium torn down to build the new one and that just wasn't proper. But money talks.