Sean Ludwig for VentureBeat:

Including the new Walgreens, FedEx Office, and Staples locations, more than 20,000 retail locations nationwide sell the card reader. The reader is additionally available at the Apple Store, Best Buy, OfficeMax, Radio Shack, Target, UPS, and Walmart. “Accepting credit cards should be as easy as buying supplies at your local store,” said Jeffrey Kolovson, head of retail distribution at Square, in a statement.

FedEx Office and Staples see a lot of small business owners (Square’s target segment). They come to print marketing materials and ship their products or to buy furniture. They are a consequent part of the clientele so it makes a lot of sense to have the Square readers there.

Regarding Walgreens, I do not know the stores at all since I’ve never encountered them. So I am not sure what the rationale is. Most probably something similar to the other two.