Remember that you lose about half a day of "outside" time with every move because of the time it takes to pack up and check out, then check in and unpack again -- so imo you lose more time by switching bases between Luzern and Wengen.
I would say to pick one and make that your base for your whole time.
Also remember that any trip up to the mountain peaks will be wasted unless the skies are clear -- you would be spending a lot of time and money to stand inside a cloud. Weather changes very quickly and unpredictably in the mountains, and the longer you stay in/near the mountains, the better chance you have of getting clear skies. The chances that you'll have clear skies on your one morning in Wengen could be pretty low.
Have fun as you plan!
Depending what time your flight arrives or leaves you could visit Zurich before or after departure/arrival. The train takes about 10 minutes from the airport to Zurich and about 50 minutes from Zurich main station (Zurich HB) to Lucerne. This would give you a chance to see the transport museum - www.verkehrshaus.ch - and the Glacier Garden - www.gletschergarten.ch - OR do an other mountain excursion (my favorites are www.stanserhorn.ch and www.rigi.ch ) the remaining day. For more details look at the Top Questions about Lucerne (TA Lucerne forum).
I was in Lucerne yesterday and zi am now in Wengen. Lucerne is a town that has an old town around chapel bridge. You can walk around the main sights in 2 hours, honestly. I also did My. pilatus (completely worth it) and that was about half- day. I think 3 days is way too many for Lucerne. Wengen is extremely beautiful. It sits right in the Alps and you can see the snow capped mountains, waterfalls, etc.very quiet village. I would decide based on the weather forecast. If the Alps looks rainy, I would do Lucerne. But if the weather looks sunny, I would do 1 days stopeover in Lucerne and still go to Wengen. Or stay in the Alps area.
Thebother thing that was tough above Lucerne was how expensive it is. W were paying $30CHF for a burger with fries and a beer. We ended up buying sandwiches from a Coop store and eating that.
Hoe this helps. Lucerne is a 1 day/ 1.5 day kind of place.
I am sorry that you did not see more from the Lucerne area. Look at the Top Questions about Lucerne for more information about things to see and to do.
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