<<"We were hesitant to travel by train as we heard that it would be expensive. Is traveling by train really that expensive ??">>
How can I answer that question? What is "that expensive" by your standards? Compared to what? If it is compared to a rental car in Switzerland, you can make a comparison.
How many of you are there? How much luggage do you have?
Renting one rental car might well be less expensive if each of you has to buy a train pass and there are several of you. However, you would need to take care to rent a car that can hold all of your luggage.....The cars that I rent tend to be for 4 or 5 people, as long as the ones in the back seat have short legs, but do not have room for luggage for more than two people, if the luggage is a couple of moderate size bags per person.. A car with a large luggage compartment would be more expensive than average.
Parking is expensive in the cities and is not easy to find. If I park overnight in Luzern at the main station (the hotels I use have no parking because they are in the "old city") , I pay on the order of $40 or $45 CHF. it has the highest rates because of the location. I note that Hotel des Alpes is on the forum's recommended list. I have stayed there a few times since the Hotel Schiff closed. The hotel is very comfortable and well maintained, with good views on the river side. It has a very good location inthe Old City. The kitchen is ordinary. I eat elsewhere...easy to do."
<<"Car parks in Lucerne Unlimited parking is set to the car parks in the city centre. Parking rates : CHF 3.00-3.50/hour, daiy maximum CHF 25.00-50.00, pending on location. ">>
And, if you have never driven in snow and ice, you really should not be learning in a strange country, possibly jet-lagged, even with a GPS. That is especially true if you have no experience driving on the right side of the road. Further, the street layout in many cities is not easy to navigate, (the old lanes and cow paths are still there, but they are now paved and called streets. ;-)
You cannot tell what train travel would cost until you lay out an itinerary. Then, Arno and Annika can help chose a discount rail pass.
As I noted above in my first post,
<<"Once you have worked out an itinerary, which can be aided by the tools in this forum, it's possible to discuss travel detail">>
By the way, don't expect a cheap vacation in Switzerland (vs. many other European countries or the USA) unless you work really hard to stay in B&B's in out of the way villages, and avoid better restaurants and most hotels in the cities. It can be done, but simply going to the major tourist destinations and staying in pleasant hotels can add up quickly. It has been several years since I regularly travelled to Singapore, and the company paid for my stays, so I don't remember the hotel costs there.
This My Swiss Alps web site has excellent information on finding good bargains in hotels, as well as listings for some of the better ones. Look at prices, particularly for those that Arno and Annika ( the forum moderators) recommend, once you have decided where you will go.
If you post a suggested itinerary, we can comment on it. Lucerne is a really good base for a first trip to Switzerland.
Bern is easily accessible by train. Interlaken is a good base for the Alps, and bern.
Lucerne and Interlaken are 1 hr 50 minutes apart by train. By car, assuming the Brunig pass is not in a traffic jam, the trip is a bit faster. It's a scenic train ride, and everyone gets to look out the window, since no one has to drive.
Zermatt and much of the alpine region near Interlaken are car free zones, with the exception that you can drive into the Lauterbrunnen Valley as far as Lauterbrunnen and Grindelwald, where you can park your car. That is a really busy time in the alpine resorts, so I don't know if the very large garage at Lauterbrunnen will fill up.....?
Let us know what your tentative itinerary is. We can work from there.