I really only take Penny into places that make it clear that pets are welcome there-- I wouldn't want to put the employees in an uncomfortable spot.
Although, several years back when I was living in Chicago, I had an extremely calm, personable pet rat. He used to ride almost everywhere on my shoulder. He went on the train with me, to stores, to the park-- I'd just plop him into my backpack and pull up the zipper when we entered an area where I thought somebody might protest his presence.
Sadly, I think my dog is a bit too large and wiggly to conceal as effectively.