First off, {{{hugs}}} I've been at a point where no one acknowledged my birthday, or attended, and it really does hurt.
I've discovered that when I have a routine, I often run into the same people in those places; it's evolved to a point where I am now in the peripheral of a group of women with whom I share a common interest, and I've been able to sign up as a volunteer for some of their projects. I would attend the public library every Monday night (free), the same women and children were there on that night, the women would disappear into a meeting room with an invitation to the public on the door...there I go. Tuesdays I worked out at Zumba...that didn't pan into any real friendships, but I got to know a neighbor lady a bit, and her son/my daughter get along so that was good. Thursdays I take the kids either to the park or a particular indoor activity center. The same kids/parents are usually at those places on that night, with a few switch outs that may be someone I recognize from somewhere else.
I guess what I'm saying is, get a routine. You'll discover after a little while that a lot of other people are routine people too, and you'll get to meetup informally, get to feel each other out and make the next move at your leisure.