You can effectively extend a touring holiday of Europe by several days and perhaps save money. To do it you need a Eurail pass and a little forward planning.
This is how it works. With a Eurail Pass you can go from city center to city center in Europe in great comfort at a reasonable price.
The key to this is the phrase ‘city center to city center’. Consider Paris. The airport, Charles de Gaulle, is 23 km north-east of Paris. If you go by taxi in either direction it costs the national debt and takes 45 minutes. There are regular buses and trains but your journey is never going to be less than 45 minutes. Leaving, you have security to go through and the airlines would like you there well before take-off. At least an hour, sometimes two hours.
Thus on any flight you find that as much as six hours, never less than four, are spent getting to the airport, checking in, flying, getting there and collecting your luggage. Then getting to the center of your destination.
By train, in every capital in Europe (I have searched and found no exception) you arrive in the center of the city.
Yes, you need to be at the train station ten minutes before the train leaves — make it fifteen minutes to be on the safe side — and when you get to your destination it is instant arrival. Your baggage is with you and you are there, bang in the center of the city. To test this stay with Paris for the moment.
At Easter — one of the busiest times of the year for Paris — I arrived at Gare de L’Est, one of the main stations of Paris. In the station was the tourist help desk — every station in Europe has a help desk.