I've been to all those cities and honestly your budget is fine, if you don't mind staying in a medium hotel (not the best, not the worst). You can budget travel in all those cities. I don't know if you and your partner like animals but if you do, Amsterdam has one of the best zoos in Europe (in my opinion), and couple that with some great architecture and sight seeing whilst being one of the cheaper options and a canal tour is pretty romantic and unique even in the cold weather. I think Prague probably has some of the best museums listed though, or Paris for art - Paris would be the most expensive in my opinion.
You might want to add Dublin to your list of possibilities - I love going there for weekend breaks.