It's tempting to try and visit too many places, but it can get tiring and it's hard to get more local flavor if you're just hitting the main sights and moving one. We spent five days at each city, and visited:
-Dublin
-Zurich
-Venice
-Florence
-Tuscany
-Rome
-Paris
-Barcelona

Lots of other good places to visit in Europe, of course, we selected these based on personal preference (e.g., Barcelona to catch a FCB game, Paris for amazing bread, etc.)

Having access to a kitchen makes a big difference when you're going on such a long vacation, since eating out for every meal gets old rather fast. Airbnb is usually a great option for this, though you can often find hotels with kitchenettes, like the place where we stayed at in Florence (http://www.granduomo.com/en/).

At this point, your question is way too broad for CB to point you in the right direction. I'd suggest making a list of things you want to see, then ask about the best cities for that, and then ask about places to stay/eat/etc where you'll be going.