You have gotten very good advice from Annika and Vasudha. I do not disagree with any of it, but, as you yourself have noted, there are personal preferences involved in some of those decisions.
So, I offer a few ideas for you to consider, based pretty much on my own personal preferences (some might say "peculiar" instead of "personal.") ;-)
If I had a choice between seeing Zürich and the Rhine Falls or riding the train over the Gotthard pass, with a boat ride the length of Lake Lucerne thrown in ( The Wilhelm Tell Express), there would be no hesitation. Skip Zürich and the Rhine falls.
[Disclaimer - I live in the USA, and have seen the American and Canadian Niagara Falls. The Rhine falls, though powerful, are not as high or majestic as Niagara. And, you can see waterfalls lots of places, but there is only one Gotthard Pass rail route.]
Yes, it means going back and forth over that route on the same day. Fine by me. However, I'd study the map and the schedules in the timetable, and I'd adjust the trip a bit to shorten it. One option is to turn around at Bellinzona.
Personally, I'd go on to Locarno, walk the short distance to the funicular up to the Madonna del Sasso, go up, come back down, walk the short distance to the lake shore promenade and "restaurant row" to have lunch, then take the train all the way back to Luzern, and skip the slow boat ride on the way back.
Flip through the images to see the Madonna del Sasso church above the city.
The "all-train" route back goes through Arth-Goldau...some trains continue to Zürich from there, other go to Luzern and on to Basel. They stop directly across from each other on the platform at A-G, and the connection time can be 30 seconds. ;-) You would have 4-5 minutes, usually.
(I might add that Zürich is my favorite city in Switzerland, but that is because I have taken many years to learn my way around. The cultural things are appealing, and that means a lot to me on repeated visits. For a first time visitor to Switzerland, I'd say it would not be high on my list of recommendations.)
I discussed this with Jane Q in a long thread a while ago....part of it relates to Zürich.
Scroll down to the early November posts for walking in Zürich.
I'd consider it for walking around on the last day before I go to the airport, since your flight is in the late afternoon.. You could even fit in the Rhine falls on that day if you would like to, and get up early..
Travel time between Luzern and Zürich Airport is about an hour, two times per hour. One requires a change in Zürich, the other does not.
There are about 5-10 trains per hour from Zürich main station to the airport. You could go there from Luzern, store your luggage, then go onwards later. Or, you could go to the airport, check in, or go to the airport, store your luggage, and go back to Zürich or to the falls.
Admittedly, it adds 45 minutes vs. staying in Zürich, but I'd stay in Luzern on my last night if it were my first trip to Switzerland. Actually, since I've been there many times, I choose to make my last night's stay in Zürich down town.. If I had an early flight, I'd stay in Zürich and use the frequent trains or 65 CHF taxi to get to the airport.. Yes - 65 or more CHF!! Occasionally higher. Once or twice it was "only" 60 CHF. My wife prefers to leave Switzerland in comfort, at any cost. I prefer to save money and haul my luggage myself on the train. We go by taxi when she is with me. ;-)
Flexibility between the Jungfrau region and Luzern -
Clear weather is critical for the Jungfrau region. Weather in Switzerland can change rapidly, and there are lots of microclimates due to the mountains. The tourist office by track # 1 in Luzern main station, as well as train stations and tourist offices near the Jungfrau, and webcams all can guide you about how to split your time between the two locations with advice on weather. . You can enjoy Luzern even if the weather is not super, but for the Jungfrau region, you will not want to spend as much time there if it is cloudy on high, so you'll need contingencies, as noted by Annika. I like Bern for that.
<<"Of course you could consider either Wengen or Lauterbrunnen instead of Interlaken. I wouldn't split your stay in the Bernese Oberland into two nights in Interlaken and two in Wengen/Lauterbrunnen though, as the towns are all located pretty close to one another and I don't think it's worth the extra time spent on checking in and out, packing and unpacking your stuff. So I'd say you should pick either Interlaken or Wengen/Lauterbrunnen for all 4 nights, before moving over to Lucerne. Interlaken's great advantage is its central location, allowing you to easily travel to several directions. Lauterbrunnen and Wengen are smaller villages, closer to the mountains and more scenic than Interlaken. Lauterbrunnen would be more central than Wengen; Wengen on the other hand offers great views over the valley in clear weather. So it's all a matter of personal preferences and convenience, and you really can't go wrong with either choice.">>
She is 100% correct in describing the tradeoffs. . Personally, I like to spend as much time as possible near the Jungfrau, because the region is full of magnificent views, easy hikes, cableways, etc.
So, i stay in Wengen, and accept the longer time needed to get out into the rest of Switzerland. Wengen,because you are in a mountainside village with unique views, and have faster access up to Männlichen has a more "Swiss" feeling to me, and I love the views that greet you ever morning or all during the day ( in good weather.....)
By the way, with light luggage, it is not a big deal to split your stay between Lauterbrunnen and Wengen.. But, I'd probably not do it unless I were on my own with almost no luggage.
Kim likes Wengen, too.
Here is her short report, which covers more than Wengen.: