Gothenburg in Sweden is notorious for having a humor that’s concentrated on word play. No other city (i’m generalizing here) in Sweden has this fixation, it’s like Gothenburg is the capital for this genre of humor.
One example that would be a home run in this city is the following:
What is the name of the one-legged woman?
Eileen.
You either love it or hate it.
Now, the question is, is there a US or UK equivalent of Gothenburg?
In the UK, I don’t think there’s anything as specific as that, no. The closest I can think of is Liverpool - occasionally you will hear about the famous Scouse wit, although usually from Scousers themselves.
"I know a woman with one leg named Eileen.’
“What’s the other leg called?”
I don’t know of any place in the US that’s renowned for any kind of humor. In a broad sense, you have regional humor (Maine humor being one example – although I’ve never actually heard it in Maine), but it’s not as if one town or county has any repute for humor, let alone one kind of humor.
Mark me for “wot?”. I absolutely dont get the joke.
I lean. (You see, she’s only got one leg…)
What´s the Maine humor supposed to be like?
And the Scouse wit?
She’s married to the guy swimming in middle of the lake - Bob. Their son Matt is currently lying on the floor by their front door. Their other son, Doug, is standing in giant hole…
I’d say that London rhyming slang is somehow related.
Is a one-legged Japanese woman Irene?
Nantucket?
Good night!
And she works at IHOP. Don’t forget to tip her.
We just had the national championship in word puns here in Sweden, and I must disappoint you by revealing that the winner was from Stockholm.
I personally know the man, and while charming, he can be a complete pain in the ass when he gets his steam up 
And last year’s winner is a colleague of mine, living in but not from Stockholm (or Gothenburg).
His winning entry was: Turken fes konstant i n Opel
not US or UK, but what about Limerick?
Tourist stops his car and asks the local how to get to Portsmouth. The local says: “Well, you can take Old Orchard Road down to Rte. 1 and then…, no that doesn’t work. OK, keep going straight 3 miles and then turn left onto Saugus highway until you get to that big red barn…, no that doesn’t work either. You can’t there from here”.
Was that his third entry?
Even more succinct:
Tourist: Does this road go to Portland.
Mainer: Nope, it stays right here.
I was going to mention this. The organizers usually do a media blitz locally around the contest… it is something to behold.