Look online at your community page.
There are also library activities every week sometimes twice a week. That can be fun also.
I do caution you, get to know the child before. I have had so many bad play dates with my own friends kids. Especially boys>
Not trying to scare you off but I was completely shocked with the bad play dates :(
When my daughter was that age I actually found a local group here on cafemom and they had mall playdates, I went to quite a few and met a couple of people that I am still in contact with.....even if there is no groups like that online in your local area even iif you go to the play areas at your local mall you will find there will be loads of women with toddlers there for you guys to interact with.