I bring Cerise with me to restaurants and shopping. I have a nice pet carrier that looks like a large purse. When we are outside I let her walk, but when we go into buildings that I know are concerned, I place her inside her carrier and zip it up. Of course she is not a noise maker either. She's a really good girl and LOVES to go!
I would suggest that you get a quality carrier with good ventilation. I see some people putting small puppies in regular tote bags, with no breathing room or air vents and that is not good IMO.