2 nights in Lucerne and 2 nights in Interlaken

Best way from Luzern to Interlaken is by train. The route is over the Brünig pass, very scenic. Do not take the longer route via Bern.
Luzern: Take a day trip up Titlis: www.titlis.ch Take a boat trip on the lake.
Interlaken: Go further into the mountains. Lauterbrunnen, Mürren, Wengen, Grindelwald. If it is a really nice day and your budget can stretch, take a train up the Jungfrau.

We are in Switzerland now and are traveling by car. We traveled from Geneva airport to Lausanne to Interlaken to Lucerne to Zurich. Some comments for you:

Lucerne-of all these cities Lucerne is a favorite. Maybe it was the nice hotel we
found in the Seeburg area (on a bus route, just 5 minutes from town center) where we found a lovely lakeside bar with lounge chairs, tables and a jazz playlist on the stereo. It's very walkable, has access to Mt. Pilatus, has the train museum, boat rides on the lake, kappelbrucke-famous landmark-an amazing wooden bridge, the Alstadt-a pedestrianized area for shopping.

Interlaken - we stayed one night there in advance of our trip up to Jungfrau. It felt touristy to me with shopping as a focus. Would agree that you might consider staying in Grimelwald or other nearby towns. They feel more authentic.

Jungfrau-don't buy your ticket ahead of time unless the weather forecast is clear for a sunny day. Go as early as possible-trains leave as early as 6:15 am or so. Take water and snacks. A bottle of water at the top is almost 6sf. If you are not used to the elevation, drink fluids and eat some chocolate while there and take it slow till you're acclimated. If you go outside to walk on the glacier, wear your sunblock. That snow is a great reflector. There is a lot going on up there. It is a bucket list kind of place. Enjoy!

Forget Interlaken and add a couple of days to Luzern.

I say this because Interlaken is Interlaken. Based on your trip I just don't think that that is where you want to "see Switzerland". Interlaken isn't bad, per se, and I have stayed there--even gone out of my way to go there. Usually to buy something because they have good outdoor stores when I have a need.

I would either add the days to Luzern (go up the mountains, swim in the lake with the young and older, take a steamer or other ship/tour on the lake) or route around and spend all your Swiss days in Ebenalp, Appenzell instead. I vote option #2--ride the cablecar up to Ebenalp, stay in one of the two (or three, if you want to hike) easily accessible berg hotels. Either way you would cut the travel day between Luzern and Interlaken out. Any travel day you can eliminate can be awesome day in the mountains or on the lake!

Good trip!

There's no such place as Grimelwald...it's either Grindelwald or Gimmelwald.

There is not need to stay in Interlaken if you came to see the Swiss Alps. travel 20 minutes farther from Interlaken Ost on the tiny train to Lauterbrunnen. THAT'S where you'll KNOW you're in the alps! Stunning vistas all around you. Interlaken is a touristy little transportation hub.

I would avoid Interlaken. We just returned from our vacation and went there one night for dinner. The main drag is very touristy. Among many things you will see a Sex Shop in plain view and a Hooters. Very odd. Stay elsewhere.