There is lots of free street parking if you don't mind walking. The Ontario Street garage or the Carlisle street garage are both only $5 and very close to the arena. If you drive a bigger car, the Carlisle street garage has smallish parking spots but the Ontario street garage has normal sized parking spots.
If you are looking to park and eat downtown, I would recommend Kully's (burgers, sandwiches, pizza and wings), Score Pizza (stone-fired pizza with unlimited toppings), Wild Wings, Hambrgr (best hamburgers around), or The Works (good hamburgers as well). Lots of people like the Merchant Ale House but I find their menu a little limited. There are lots of other restaurants downtown but those are the ones I have been to and liked. If you are looking for something really quick, there is a Subway and Pizza Pizza right by the Rankin Bridge.