Studies have shown that new arenas do not give that big a boost to a city's economy. A new arena simply shifts the location of where the citizens of that city spend their disposable income.
I don't want to get too political here, but isn't national defense exactly where public dollars should be spent? You can argue about how much to spend, but using tax money for the military is a legitimate public expense.
Not taking sides.
You will get arguments that defense is the least productive way to stimulate an economy. Infrastructure, roads, etc. and even arenas, are more productive as a stimulus and therefore more deserving of taxpayer dollars. It has to do with how fast dollars are cycled. What is more important, economy or security?