How much time are you planning on spending? Because, you know, take any of the big cities—Rome, Paris, London, Madrid, Berlin—all of them can keep you busy for weeks. Just the
Musée du Louvre in Paris (I'm assuming you were able to tell that musée means museum) has over 60,000 square metres worth seeing. If you're going to go, make sure you ask yourself what
type of thing you really want to see and then make a list of things.
I don't even know very much about Europe (just Western Europe, really) but I think you should have a look at the list of
UNESCO World Heritage Sites. All of the things on this list are amazing and historically significant in some way, yet not all of them are gigantic tourist traps. You need to see the Eiffel Tower and the Guernica, but you don't need to hop only to and from places that you've seen on TV. Go to
Kinderdijk,
Cáceres,
Mérida,
Abbaye de Sénanque. Go to the
Tom Simpson memorial on the Mont Ventoux and watch as the runners of the
Tour de France crawl by. Go to
Ravenna and walk on actual mosaics.
To feel a little closer to the people who inhabit the countries you're visiting, you don't need to just visit things that people at home will recognize when you tell them how your vacation was. And it'll be a lot more serene that way, too.
One tip, though. If you're going anywhere near the southern part of Western Europe (Spain, France, Italy), don't be afraid of churches. Even the local churches in the tiniest villages are amazing. This is the center of catholicism, funded by and made out of gold stolen from Latin America (sorry, guys) and the denarii of the poor. I say you should have at least a peek in every church you find. They almost always have free admission, too.