14 stops in 42 days works out to an average of 3 per day, which is pretty good. I suggest 4 days in Paris, London, and Rome (probably Prague as well though I have not been there); 3 days in Cinque Terre, Munich, Florence, Nice, Barcelona, and Amsterdam (though if needed you could cut to 2 days there); 2 days in Venice. Don’t stay in Monaco- see as a day trip from Nice (it’s super easy by train or bus).

Dreaming of Italy got it perfectly right. Nice is a great city, but you may find staying in Antibes, Cagnes sur Mer, Ville Franche sur Mer cheaper. The beach at Nice is smooth rocks, some of the other cities have sand beaches.

I think a railpass will save money for this trip. I would look at a cheap flight from Barcelona to Nice and perhaps point to point tickets, either all the way or at least from the Czech border to/from Prague. You may also find that a point to point ticket for one of the legs in Italy is cheaper than using a day of a railpass. I would compare a 30 consecutive day pass (validating it when you leave Nice and having the 30 days end when you arrive in Paris might work), a 15 day flexipass and a 5 country (France, Italy, Switzerland, Germany Benelux) select for around 12 days to see which works best. What does the trip planner recommend for a railpass?