In NYC it is pretty common for a mom & pop bodega to either not accept debit and credit, or have a ridiculous limit on it. The pizza place I used to eat lunch almost everyday was $25 minimum for cards. The bodega next to my office was $15 minimum. The bodega under my apartment had $5 minimum, but they usually waved it for me if I was over $3 and didn't have cash.
Also, almost every Chinese restaurant or Ramen place had Cash Only signs.
A rewards credit card costs the business your shopping at 2%, or all the way up to 3.5% for certain cards. Then you get network fees (from Visa, Mastercard, etc) and another few cents and tenths of a percent tacked on by the businesses Payment Processor, and poof, there goes 3% of their income!
Its no wonder so many businesses don't take credit cards or debit.
Also, almost every Chinese restaurant or Ramen place had Cash Only signs.