For most travelers, I recommend taking the train. Most people visit cities and a car is an expensive nightmare in any city. If you stay in the suburbs to accommodate the car, you waste a lot of time and money commuting to the “sights” using public transit. Renting a car is a great way to explore more rural areas and I highly recommend it for short periods if your budget can handle. The French Riviera is a good place to rent a car IF you’re interested in visiting the tiny villages in the Alpes Maritme and Provence above the coast and are not intimidated by narrow mountain roads and ultra-aggressive French drivers. If you just intend to visit the coastal cities and beaches, they are connected by fast and frequent trains — which generally offer better scenery than the roads. The area around Florence or perhaps between Florence and Venices is another place where a rental car would be fun. However, you won’t want a car in Florence and can’t drive one in Venice (or Amsterdam).

There is excellent train service to all of the cities in your itinerary — although you may want to look at flying to/from Krakow as it’s a bit out of the way. Train will be faster than driving and probably cheaper. It will be more convenient for the cities you’ve mentioned. Rule of thumb is $ 150 per person per week by train and $ 500 per week for a compact car. Thus, for 2 of you, train will be cheaper, for 3 it’s about a toss-up although train is probably still cheaper if you need to upgrade to a larger vehicle to accommodate full sized people and gear. For 4, car will probably be cheaper, but still less convenient if your main focus is cities.

thank you so much for your help.