Biking canals, museums.
Eiffel Tower, Louvre, pastries.
Colosseum, Vatican, gelato.
Baths, Fisherman's Bastion, chimney cake.
Skiing, chocolate, Matterhorn.
Dutch pancakes, Van Gogh museum, Anne Frank house.
Palace of Versailles, Disneyland, crepes.
If you have more time, consider adding a day trip to Zaanse Schans windmill village or Keukenhof Gardens in the Netherlands. In Paris, the Catacombs is a unique and fascinating choice. Roma Pass can save you time and money on attractions in Rome. In Budapest, take a sunset cruise on the Danube river. In Switzerland, try ice skating or tobogganing in Interlaken or visit the city of Bern.
If you have less time, consider reducing your time in Amsterdam or Paris by a day or two. Another option is to fly directly from Rome to Budapest or skip Switzerland altogether.