Ahmad
I assume you have never been to Europe and will suggest a couple of popular destinations which i assume would be relatively easy to fly in and out from Lebanon.
Fly to Venice 4 nights
Train to a ski resort in Italy or Switzerland 3 nights
Train to Paris 5 nights
Venice and Paris are great first time European destinations, and personal favourites of mine.
You could spend all 4 nights in Venice with a day visit to Verona or move and spend one of those nights night in Verona.
I have never been to the Alps, but there are ski resorts in Italy and Switzerland. I have excluded Austria because it is going the other direction from the final destination. Others here may be able to suggest specific ski resorts. I only budgeted 3 nights and 2 days because i would assume that is about all a new skier or a good skier skiing with a new skier will tolerate before getting on each other's nerves. Or you can move the 4rth night from Italy to here if that is your preference.
Long train ride to Paris which will take up most of a day. 5 nights gives you 4 full days in Paris. If you want to break up the train trip, consider spend one night in Lyon. Lyon is on the way and very lovely. However, my preference would be to get to Paris sooner and to spend the time there.
I like to avoid zigzagging or doubling back whenever possible. I also prefer staying in one spot and enjoying my time with my feet on the ground instead of my butt in the seat of a plane, train or automobile. In terms of where to stay and eat and what to do, there are just too many possibilities to list. You can research from travel books or websites and make a list.. If you have specific questions anout a particular hotel, restaurant or attraction, somebody here will probably have the answer for you. Have fun.