Puzzles for toddlers are great. My child loves them. Also parks, inside play places if weather is bad. Also I love to play with him on the floor, crawling and chasing. I don't know what city and state u live in, but learning centers, petting zoo, Zoo, helping mom do housework Is fun for them also. I let my little gut help me with what I'm doing to teach him. So many things to do, that's a fun age!
Go to a park, look at a pet shop, play with Playdoh (like Astrid said), or buy him/her a small (unbreakable) instrument and play it with him/her; learning music is a VERY good thing to do. They say that kids who learn music tend to be alot more intelligent than kids who only play sports and things like that.
There are tons of things to do!
I'm going to have a nephew in four weeks and I can't wait!
Library story hour, apple picking, craft projects, make your own playdoh recipe online, make cookies or decorate some sugar cookies together, sidewalk chalk, string beads or do lacing cards, dance and dress up, swim lessons at local y or college or ? , tumbling class , etc.