Sukhumvit Soi 5. Walk away from Sukhumvit for about 100 meters and look on the right hand side. You will see a laundry sign.
Tiny little place, not much more than 5 square meters. It occupies a tiny corner of a foot massage/male grooming salon.
It's run by a very nice, straightforward lady. Prices are 100 baht per kilo for wash and dry. Ironing is extra per piece, and not especially expensive.
You collect your clothes 24 hours later. They also have an express option if you need something doing the same day.
Careful, you will walk past it if you are not paying attention.
https://maps.app.goo.gl/YraxXZShSbQpMomK9