I've taken a 12-pound foster pup with me to various clothing stores (Nordstroms, Macy's, Ross, and Neiman Marcus), coffee shops (she could come in while I ordered but we had to sit outside), Target, Sephora, etc. Some places would offer her water and even treats! -But my city is known for being animal friendly. Many stores (Lululemon, Haagen Dazs, and Michael Starts) have communal dog bowls by the entrance.
I say just call in advance to not risk the embarrassment of being asked to leave.