Contrary to what many Americans think, teenagers in Europe dress pretty much like American teenagers. For both of you, I suggest walking or running shoes that you know are dependable and comfortable enough to walk in for hours at a time. I.e, of you wear a favorite pair of shoes every day, all day long, back home, that's the pair to take.
Otherwise, you will both be walking around in "stylish comfortable shoes" wondering why all the locals are wearing shoes like you wear at home.
If you can afford the luggage space, pack a dressier pair for the odd occasion.
Don't even try to disguise the fact that your are a tourist. Everyone knows, and they don't care.
Convince your daughter to be practical. if she isn't, she's likely to develop blisters on her feet on Day One, which will make Day Two and all the rest pretty miserable.