You'll be doing a LOT of walking and typically, hiking boots are not really the best for traversing city sidewalks. On the other hand in nasty weather they'll (presumably) keep your feet a little more dry. I don't know what kind of hiking boots you have, but I'd NEVER bring mine to Europe unless I was planning on doing some heavy-duty forest hiking.
Bring some good, stout shoes that will keep your feet at least mostly dry in the rain or snow and have a bit of tread on the bottom of them. Probably with nasty weather it's a good idea to have a stand-by pair handy, but if you want, you could always get them over there as a souvenir of sorts instead of bringing them with you.