Chucky Cheese or Ben and Jerry's...lots of fun, little structure, 2 year old heaven!
Luckily, 2 year olds don't need as "long" or "detailed" party as older kids, so a good hour or hour and half at either of these places will be perfect!
Also, how about the place called "Charlotte at Play" (an indoor playground that I think is geared towards younger kids).
And, Discovery Place is wonderful with young kids! They have open areas for the kids to see and learn about animals, but it's not over the top. They also help with birthday cake, drinks, etc. And, it's nice and cool!
Good luck!