At a dance.
I used to take lots of lessons at a ballroom, and I would social dance ~3 times a month there. I built a large network of casual friends there. My ex-wife worked there (after we were married) but quit in anger. I was banned from going there by my ex. A few days after filing for divorce, I went back to that ballroom for entertainment, to share the news with my old friends that I hadn't seen in a year or two, and just for comfort.
Sitting at the table with my old friends was an cute, smart, fun young woman. She was there for the first time and just happened to land at that table (my friends are quite welcoming to newcomers). We hit it off (both loved to dance, both have similar personalities, both chemical engineers, both with graduate degrees, etc). I was highly attracted to her but I was really NOT in the mood to start dating. I spent half of the time getting to know her, and half of my time sneaking behind her back to tell my friends of my coming divorce. She left in the middle of one of those conversations - I didn't say goodbye, didn't know her last name, and didn't know her phone number. She figured I wasn't interested since I wasn't hitting on her.
Two months passed and I kept going to that dance so I could meet her again. I couldn't get her off of my mind. Eventually she came back. I was now ready to date. We talked/danced all night. I made certain that I got her full name, phone number, and even a little peck on the cheek.
20 months so far and we are doing quite well.