There are many people out there who hate the idea of public tax money being spent building new facilities for professional sports teams. I've listened to Bill Simmons and Malcom Gladwell repeatedly lament any tax revenue being used to subsidize some "rich guy's new toy". Recently plans to build a new arena in Calgary have seemingly collapsed while Ottawa could also benefit from a new facility downtown.
I'm less enthusiastic about tax money being used to fund 100% of the cost of a new facility, but if you can get the team owner to split the cost, then why not set terms and conditions on that public money? Instead of building a new arena, build a new state of the art community center that is also an arena. You can require the building to have certain things available for public recreation or municipal business. Perhaps you could build a high-performance training center for various youth sports, studio space for the arts, offices for Municipal departments, gym space, etc.
Require a certain amount of square footage dedicated to things the public can use for their enjoyment and betterment, and require a minimum number of hours that facility must be available for public use. Obviously, there is a cost issue involved as you want to add more functions to the building. You can't just build a mega-structure that has a home for every recreational endeavor (but that could be a future blog post). There will need to be a process by which the specific needs of the community are identified and prioritized, then planned out in the most efficient way possible. Maybe it starts with a simple "wish list".
I don't see this as taxpayers buying a rich guy a new toy, but rather an opportunity to get a rich guy to invest in a great new multi purpose community center that the local people will enjoy for years. This doesn't need to be seen as an evil thing. Tell the owner, we'll pay half, but here's what you have to do. There is a way to benefit both sides. Especially if Calgary intends to make another Olympic bid. That would give the owner a bit more leverage if the city suddenly needs a new rink.
Prepare a list of demands then get the rich guy to help you build what you want. There are so many things that you could require. Have the building designed so that it can also serve as an operations command center and refuge for people in the event of a natural disaster. If you're lucky enough to have a billionaire in your city willing to share the cost of building a new community center downtown, there's a way to make it happen.