I've taken Molly in her Kwigy-Bo bag in various stores that I don't think allow dogs normally. Fortunately for me she's quiet.
I do have a really nice dog stroller for her. I've used it at dog meet-ups and parks and have gotten almost more interest in her stroller than in her! lol I have heard that you can get away with malls and stores while they're in the stroller; I myself have never tried that though.