Where is Square's major market penetration? I'm guessing SF and NYC, but in New York City I think I've only seen it used in one store, and even there I'm not sure the system they were using was Square. I know they also ran a trial handling payments in city taxis, but that trial only tested 13 cabs, and was pulled shortly after starting.
Anecdotally, about a third of small businesses (cafes, food trucks, etc.) use Square here in Austin. Another third use PayPal or Intuit. The rest use something else. Square has plenty of retailers here, and cab drivers often use Square to pay 2.9% instead of the ~5% their companies charge them to accept cards.
That sounds like a pretty biased sample. I'd be surprised if square has more than five percent of the market in any identifiable geographic region, even SF, hell, even within a mile of their headquarters.
I think about half the coffee shops in Seattle take Square.
It is SUPER ubiquitous when you go to a comic book convention; anyone who is at all serious about sitting behind a table selling their comics will have a Square reader. I'm one of those people, and we LOVE Square because it's made it a lot easier to make a sale.
When I go to the local farmer's market, a lot of the people there use Square as well. There's a fair number of clunky single-purpose credit card devices, and some other credit card acceptance methods that work much like Square, but over the past year or two I've seen people mostly shifting to Square.
Note that the two classes of itinerant merchants I cite usually don't work with Wallet; that requires having a fairly permanent place of doing business.
I find them most often (and useful, it turns out) in really out of the way places. I live in a town of 800 people in Montana -- 2 of our 4 food establishments use Square (a BBQ joint + a Pizza place). I've also purchased Lobster Rolls on remote, tiny Maine islands with Square.
