Question: things to do with a two year old on a rainy day?
Answer: The Library. This is an obvious one, right? ... 
The Local Mall. ... 
IKEA. ... 
Pet & Aquarium Stores. ... 
Indoor McDonald's (or other restaurant) Playplaces. ... 
Local YMCAs and Recreation Centers. ... 
Conservatories. ... 
Indoor Play Spaces & Playgrounds.