Unless I convince him to team up with me against you...all's fair in a snowball fight Leon.
First off - forget Chuck E. Cheese. Save yourself (and all of us) the migraine. And then maybe one of your friends who has a yard and can probably help arrange for shit kids like to set up in it can be arranged to help you out hosting it at their place and splitting the cost.
And yes I know for a fact that my yard is big enough for a full sized bounce house. No I'm not going to tell you why I know that.