If they use our money, we should get free tickets, concessions, and parking. Who pays for that stuff at a building they paid to build? NOBODY
It's always your money, man.
For the Cowboys new stadium, the City of Arlington took out $150M as a direct loan to Jerry Jones. It was secured by all of the ticket and parking taxes collected at the stadium, and if there was not enough in a given year to cover the debt service, the Cowboys were on the hook to make the difference up.
Those sorts of deals are not terrible IMO, as long as they are structured so that the team is on the hook if enough money doesn't come through. It is essentially a loan to the team, but once the receipts cover that balance, the municipality does make out in the end.
Public financing that can help front some costs BUT protect the municipality can work , if done thoughtfully. But that is very rare, and most of the time the deal is very team slanted.