I am a deeply antisocial person (that sounds terrible, I'm not rude or belligerent, but I much prefer my own company and the company of people I've got to know over the course of years (by osmosis)).
When DD was five weeks old I started going to baby groups, from 5 weeks to 11 months old we went to two baby groups a week, baby sensory, music classes, swimming etc.
Until she was four months old or so, she couldn't have cared less where she was, or what we were doing - those classes were definitely for me. From four months on, she seemed to actually enjoy the classes, smiling and clapping, and bouncing up and down to the music.
I've met one person I'd actually call a 'friend' at these groups, but their real benefit is giving me loads of people who I say 'hello' to as we pass in the street, or stop for a chat with if we meet in the park. I found maternity leave pretty overwhelming, so that sense of community and commonality was really helpful to me. DD is now 14 months old and is at nursery four days a week, when we're walking through town on one of my days off, I still run into people I met at baby groups, and still stop for a little chat, and that's actually really nice (especially living in London where it's all too easy to be anonymous).