One word: activities.
You don't want to meet "random" people. You want to meet people with whom you have a connection. What better way than to engage in some enjoyable activity that is done with several people? There are clubs for hiking, clubs for knitting, clubs for cycling, clubs for helping the needy, all kinds of activities that you can engage in as part of a group. Even if you don't hit it off with someone special, the people you will be hanging out with are people you already have something in common with.
I did this as a conscious strategy aimed at finding a partner, by joining a hiking club. The worst case would have been that I would spend my weekends doing something I loved to do. As it turned out, I met my wife on top of a mountain, and we have been married for 15 years. Because we both had a connection to the same activity, we shared similar values, and she has stuck by me through my transition.