Huxley, half of the centre Edinburgh is cobbled! I was scratching my head trying to think of where you mean but I reckon you're talking about Greyfriar's Bobby: http://en.wikipedia.org/wiki/Greyfriars_Bobby. He's not quite a bear but, famously, he's been waiting by his master since 1858, so he's still there if you want to visit him!
Well after a nose on google yeah must be rose street, it was years ago anyway just wondered if that bear was still lumped outside as i had a great guinness and pizza there.