Annika and Tulips SXV -
Does the Brienzer Rothorn fit? I did not work the timetable, but it seems like a long trip from Luzern.....
Just checked the timetable - 2 to 2 1/2 hours from Luzern by train or less than 2 hours by the back door - the train to Schüpfheim in the Emmental, then the bus to Sörenberg and the gondola car lift.
I'd take the train to Brienz at least one way, probably both ways, personally . The train up and down the face of the Brienzer Rothorn is a major highlight of the trip.
So- the route is Train - Luzern to Brienz. Walk 30 meters to the station of the Brienzer Rothorn. Take Brienzer Rothorn Bahn to the top.
The weather up there can change rapidly. Wear a windbreaker and carry something warm for layers. We went up on a sunny day once, plannin to hike to Schönbüel and then take lifts down to Lungern, walk 20 minutes uphill to the train station, take train back to Brienz (or Luzern). When we got up to the top, it was cloudy, windy and cold. Did not hike. Had a coffee instead. Got back down to the bottom eventually and it was sunny again.
Regarding Luzern, Bern and Basel -
The trains between those 3 cities are all one hour duration trips or less (for the fastest trains once per hour or even twice per hour)...well, one hour +1 minute Luzern to Basel....so that doing two cities instead of one adds one hour of train time. Many trains have restaurant cars. Or pick up a sandwich and eat on the train.
My own opinion is that Bern+Basel in one day is a bit much, but if I were forced to do that, I'd walk from Bern main station through the old town with the arcaded streets, fountains, and clock tower, cross the Nydegg Brücke (check to see if the Bear Pits have been re-opened after maintenance), walk up to the Rose Garden (food, too), look at the flowers, look out over the city, walk down again to the old trolley barn by the Nydegg Brücke (it is now a restaurant) for a beer and a sausage, and catch the tram back to the main station from in front of the Brasserie Bärengraben.
Elapsed time - 2 to 2-1/2 hours at a leisurely pace.
I'd miss a lot, but I'd have the feeling of the old town.
Its museums are a particular strength, so the following leaves time for a little bit of unspecified museum touring:
From the station walk down to the old city and town hall, past the #1 tourist attraction in Basel - the Tinguely water sculpture. Stop and stare. Continue to old town, walk back up to station after time in old town. (or, a tram back to the station.) Elapsed time - one to 1 1/2 hours.
Museums - Tough to fit in something from the wonderful museums. The Rietberg won't fit easily (unless you are quick with the trams or use a taxi), but the Rietberg is an unforgettable experience, no matter what they have installed for the current exhibit. It is almost out of town near the German border on the Klein Basel side of the river.
Or, the Kunsthalle is close to the old town and station and on tram routes.
In both cases, when you try to see both cities, a lot is being missed. Unless you are a museum goer, I'd tend more toward Bern than Basel. The old city and the setting on the Aare river have a lot more character and charm for my tastes. I find Basel to be much like any modern city. It does not have any special charm for me.