You say your parameters are that you must arrive in Paris, be in Prague and depart from Rome. It would help to know:
- How much time you want/must spend in Paris and Prague?
- Do you want to spend time in Rome? If so, how much?
- Have you been to Europe before? If so, where and what do you like, what didn't you like?
- What are your interests - food, drink, history, art, architecture . . . ?
- Christmas markets start up around the last week in November in some cities. Are you interesting in that?
As a general "rule", take into account that you lose about 1/2 day every time you change locations (packing/unpacking, checking in/out, getting to/from train stations or airports, lead time at airports for check-in, security, luggage, boarding). So 3 nights in a place really means only 2 days there. Are you counting 16 days from JFK to JFK or 16 days on the ground? Most of the time, flights to Europe are overnights. A direct flight to Paris is a 7 hour flight. You'll be lucky to get 3 hours sleep, so your first day in Paris, you'll be sleep-deprived and dealing with a 6 hour time difference (i.e. jetlag). Most flights from Europe leave in the morning, so you can't count your last day as "a day on the ground."