Basel Airport to Lucerne city center for two nights and then to Bellagio

Train. Pack light and be prepared to handle your own luggage.

Definitely train. There are frequent direct trains from Basel SBB to Luzern, taking just over 1 hour. There are a number of good hotel options within walking distance of the Luzern train station for your time there.

From Luzern to Bellagio, my own “best”:would be the Treno Gottardo that goes over the Alps on the Gotthard Pass route, rather than the fast intercity trains that go under the Alps in a tunnel. This train departs Luzern for Locarno every 2 hours. I suggest the 9:18 departure. You will not ride all the way to Locarno but will disembark at Bellinzona at 12:00.

From there, you will take a train heading to Milan, but you may get off sooner, depending on your route. Options:

Ride to Como San Giovanni, get off the train and make your way to the ferry dock for a ferry to Bellagio. This is the slowest option, but the fewest changes.

Or, ride to either Monza or Milano Centrale and change there to a train heading to Varenna-Elsinore on Lake Como. WLk down to the ferry dock and take a ferry the short distance to Bellagio.

As mentioned, train. Although the big question in my mind is why are flying to Basel if your destination is Luzern?

That is a good question. We are on a Viking Cruise that leaves out of Basel and wanted stay 5 days on the front end to visit Lucerne and Bellagio. In hind sight I am thinking we should have flown to Zurich but were working with Viking and they were not helpful. Then from Bellagio we were taking train out of Come direct back to Basel to get on boat. We had also thought about hiring a private car (Day City Trips) to take us from Lucerne to Bellagio as we are staying in a Villa there. Thoughts

You can also get a bus from Como S. Giovanni station to Bellagio. Going back to Basel, you will have to change trains in Zurich. There is a train to Zurich from Como S. Giovanni every 2 hours. Another option is to take the ferry to Varenna and take the hourly train to Milano Centrale. There are 6 direct train every day from there to Basel.