Well, off the top of my head:

• There was an episode of Dr. Who during…I think David Tennant’s career? It was one of those that didn’t actually have much of The Doctor in it, some guy had noticed The Doctor appearing throughout history and wanted to try and meet him, so he managed to run into Rose’s mother, at a laundromat. Who proceeded to flirt with him as she loaded her underwear into the wash by saying ‘and here I am flashing you me knickers.’

• There was a show from the 90’s that no one remembers called Relic Hunter. In one episode miss relic hunter, her assistant and I think the client of the week duck into a laundromat as a place they can look through a dossier, but the owner insists that they have to wash something to remain on the premises, because they needed an excuse to peel Tia Carrere to her skivvies.

• The episode of Futurama where…let’s see if I remember this right? Bender gets mangled and paralyzed, meets Beck, hires him as a washboard player(?) and then the rest of the cast follow him around on tour, there’s a scene where the crew is hanging around in their underwear while all their clothes wash, and it accidentally tie dyes them because of Amy’s pink track suit.

• Early in Friends, there’s an episode where Ross…again let’s see if I remember this correctly…Rachel was a rich girl and thus had no domestic skills, and Ross offered to teach her how to do laundry, kind of as an excuse to hang around with her to flirt. They also manage to accidentally dye her clothes pink by leaving something red in with them. IIRC Joey mocked him for his choice of Totally Not Snuggle, so he bought a detergent called Uberweisse or something. I think this was in their building’s laundry room rather than a laundromat but meh.

• I think there’s a scene in Dr. Horrible’s Sing Along Blog where Dr. Horrible and whatever Felicia Day’s character was named where they flirt in a laundromat. My memory of that show has kind of faded to just the Bad Horse song.

I feel like it’s kind of a meet-cute trope in older sitcoms