We have a naughty chair at home, outside we take a time out, whenever or where ever it's necessary. My son knows that if I start counting to three, he's very likely to get a time out. So he usually stops the naughty behavior before I get to three. That said, we've had time outs on sidewalks, in the library, at the drugstore....just to name a few of our more colorful locations.
I think the naughty place can move where you go, it's a concept that they get, not necessarily the location. (Though I do agree, that the naughty space at home should not be the bed or the child's room, there definitely is a bad association there, my guess is that the stroller would also create a bad association.)