Suggest another city to visit as well as depart for return to USA.

Come to Budapest it's a cheap discount airline nonstop flight away and half the cost, for the most beautiful capital city in Europe.

https://www.google.com/travel/explore?tfs=CBwQAxoeKABqDAgCEggvbS8wOTV3X3IMCAQSCC9tLzA2bXpwQAFIAXACggEECAQQApgBArIBBBgBIAE&tfu=GgA

Ahem. Sorry Mr E, but Budapest is not in Switzerland

Rather than spending half a day flying half way across the continent, you could just train to Lucerne in a lttle over an hour for a couple of nights, then train to Zurich for the flight home.

We only plan on remaining in Switzerland a maximum of 3 nights.

What is your itinerary?

a different city with an international airport terminal in Switzerland

I will be interested to see the responses to your post. I am looking at a cruise ending in Basel and I don't like the flights and connections back to Northwest Arkansas. If "any" Swiss city will do, I suggest you look at the options for flights home from various airports. IMO nothing ruins a great trip like bad flights and connections home.

Switzerland is a small country. Zurich and Geneva have direct flights to/from US cities. Lucerne is a beautiful city to spend a few days and close by train to Zurich.

Absolutely Luzern is the place to go. It's about an hour and a quarter from Basel by train and has all the mountains you need. Plenty to do for three nights. From Luzern you can take a train to the international airport in Zurich in another hour and a quarter. Easy. I suspect that your cruise offers such an excursion although at a significant cost over what you can book on your own.

Silly me, i thought the OP wanted to visit Switzerland for 3 nights then go some place else. If all you have is 3 days in Switzerland, one stop is enough. Night one, arrival day. Night two, after one full day in Basel. Night, three after a road trips some place else?, then the next day you leave? That wouldnt work too well for me.

I have a tour ending in Innsbruck. I’ve chosen a two night stay in Lucerne before taking a nonstop flight from Zurich back to the United States. I’ve visited Lucerne a couple of times already and find it quite beautiful and convenient. For me it’s less expensive and faster to fly from there than other nearby international airports.

I'd check fares home from both Geneva and Zurich. They might be significantly different. Zurich is definitely closer to Basel, but you can get to Geneva in about 3 hours, so I would consider it for the right savings. From my area, Zurich is a cheaper airport, but I don't assume that's true everywhere.

If Geneva turns out to be a cheaper or otherwise more attractive option for a flight home, it doesn’t really matter that it is a bit longer train ride from Basel, as you will make overnight stops on the way.

The possibilities if you choose Zurich, as noted, include Bern and Luzern. Even the Berner Oberland, but you would spent more time and money on trains.

For Geneva, main” route is Basel—Bern—-Fribourg—Lausanne—-Geneva ( possibly stop in Morges or other small lakeside town for the night before your flight). Any of these towns would make a nice overnight stop.

The other route goes on the north side of Lac de Neuchâtel: Basel—-Biel—-Neuchâtel—-Yverdon-Les-Bains—Lausanne—Geneva. Also some nice places to stop.

Take your pick—would you rather hear German or French?

Swiss has a daily nonstop from Zurich to Denver, so Luzern the fly home from Zurich is the obvious answer.