<<"As you all suggested .. I cut one night in Zurich .. We will be reaching Zurich from Venice late night .. We will stay that night in Zurich and then leave for Lucerne the next morning..So we have now 3 days in Lucerne .. :)">>
Hi swatiraj -
Earlier, I had assumed that you were flying into Zürich airport.
If so, that plan makes good sense, depending on how late you arrive.
However, if you are coming by train, trains from Venice seem to pass through Milano Centrale. If that is the route you are taking, travel time to Luzern is essentially the same as travel time to Zürich.
All those trains, whether they go to Luzern or Zürich, pass through and stop at Arth-Goldau in Switzerland.
You can see that in the timetable:
At Arth-Goldau, every other train from Milano Centrale goes to Luzern. The ones in between go to Zürich. So, if you are on the train that goes to Luzern and want to go to Zürich, you get off at Arth-Goldau, walk across the platform, and get on the waiting train that goes to Zürich. If you are on the train that goes to Zürich, stay on it.
If you wish to go to Luzern instead, just use the opposite procedure. Going directly to Luzern could save some transfer time in the morning. Of course, you might wish to take a short stroll before going on to Luzern, but with limited time, that might not be a good idea.
Picking up an extra day does not mean that you must spend it in Luzern. You might also spend it in the Bernese Oberland.....near the Jungfrau or at Thun, whatever you prefer.
Each of the mountains discussed has its own personality. Checking the links provided earlier in the thread can help you decide between them. The Jungfraujoch is the most impressive and the most expensive.