Men don't approach me all the time. I have a large circle of friends and am active in my neighborhood so it's not all that hard to meet people. I don't live in a suburb where I am closed off... I live in an artists community that is urban, walkable, very active and filled with LOTS of people. I am very active in the small business scene so I meet lots of people there too. I live in a "hip" historical group of brownstones with lots of people my age that don't have children so my life is a bit different than those with children. The entire vibe of my neighborhood is very friendly so it's easy to meet people and just say hello.
I happen to meet lots of people at the hospital where my sister works as we have dinner together several nights a week during her break. I also go there for many of my medical needs. If you need to be at a hospital might as well make some friends!
