Check out Charlotte at Play. My almost 2 year old LOVES going there.
Charlotte at Play
If you are a YMCA member and have a water baby, they also do birthday pool parties. Rays Splash Planet also has indoor birthday pool parties.
Make sure you stay away from Chuckie Cheese and Monkey Joes for a two year old. We have been to birthday parties there and they are not suited to a 2 year old.
If the weather is nice, you can always look at a Charlotte park. Most of the parks have a covered picnic area (and of course the playground).