They don't work, but they're there.
These wooden phone booths are in Sam's, the old time pizzeria on Court Street near Kane. It's one of the last holdouts of the old Italian neighborhood. The pizza's pretty good, the service a bit huffy and eccentric. There are red leather booths and you can get a Rob Roy.
As far as I known, these are the only extant wooden phone booths left in Cobble Hill/Carroll Gardens. Please let me know if I'm missing any.
Wooden Phone Booth Sighting: Chumley's