I take Daisy pretty much everywhere with me except if we go out for dinner or movies (it's too long).
She stays in her carrier (which looks like a purse) most of the time but you always have those curious people [cashiers, waitresses, etc] who'll see my bag ''move'' and want to see her to ''ooh and ahh''.
The other day, I had to run some errands and went to the post office to mail something so I had Daisy in her carrier and proceed to the register. Good ol Daisy pops her head out and one employee saw her and said ''CUTE!!!". I'm like, "I wasn't sure if it's okay to have dogs in here so I placed her in the carrier." The employee then said, "We're not supposed to, but it's okay, she's small and in her bag.''..So it goes to show you that there are exceptions as long as they're nice, understanding people.
I think as long as you keep them in a carrier, most places wouldnt mind or wont even know.