S.R.
Depending on which side of town you are on, the Warren Community Center has a pool and they have many parties there.
There is also Castaway Cafe in Howell and here is a link to their website: http://castawayplay.com/?=
If you have never heard of this place, it is awesome ~ a two-story play structure for kids (and adults) to burn off a lot of energy. They have big comfy chairs right near the playstructure so you can watch the kids. They have enclosed rooms for parties. Their food is reasonably priced and healthy and very good tasting. Their security is unbelievable and they mark everyone's hands with the black light ink, so no one can get out without the correct parent.
Garden City has their Community Center off of Merriman Road and from I have heard, they offer a pretty good package for birthdays.
You might want to find out if someone in the family is a Member of the Knights of Columbus or another organization because you can rent their hall. I know that the VFW Hall on Joy Road and Middlebelt will allow you to bring in your own food (had my wedding reception there) and they also have many numbers to different caterers. Than you can go to the dollar store and buy a bunch of inexpensive games and goodies for the kids to play with. You can also purchase a couple of decks of cards for ALL the adults.
Good Luck and remember at the age of 3 your daughter won't remember this, so you are really having the party for the adults.