W.T.
I'd recommend Imagine That in Florham Park. It's a really, REALLY fun place -- there's about 30 "rooms" (walls 1/2 high) and each has different things like musical instruments, a pretend post office, a house with a cloth/plastic garden for the kids to plant, plus a room full of real vehicles -- fire engine, airplane, motorcycle -- that the kids can climb on, push the buttons, etc. I haven't had a party there, but they run them all day long and they sound fun -- you get to choose from a dance party/puppet show/face painting that's just for your party.
It's off of Route 24, just south of route 10.
BTW, I've taken my 17-month old there with his brother who is 4, and it's hard to say which had a better time!