H.B.
You know what, my son, who will be 4 this winter, is begging me to have his party at Chuck E Cheese, and I'm considering it. As much as I cringe and don't enjoy the place much myself, a little friend of his had her party there a few months ago and the kids all had a really great time. The mom decided to have it on a weekday (much less crowded) and didn't do the official "party" but bought a bunch of tokens for all the kids, paid for pizza and drinks, and brought their own cake. It just so happened that another child had the official "party" going on and my son's little friend was just as happy watching the performance they put on for their group, as if it was all for her.
Another idea is to rent a room at a community center, we've had friends do that too, and you can bring some games and fun things for kids to do, food and cake, and it worked out really well and was cheaper than a "party place".
Good luck!