Winter Activities for Bern, Basel, and Zurich

I'm interested in this too.
I don't know much about the cities, particularly Basel, but I imagine there is plenty to do beyond museums.
One suggestion I would make is to plan some train trips out of the cities in the morning, so you can be back late afternoon/evening for the markets.
I hear Winterthur is beautiful and I might make that a day trip out of Zurich.

Your first sentence is confusing to me. Are you actually spending a night in each of those places, or visiting during the day?
Having one base is much easier, as it's so close to train around.
Where are you flying in and out of.? Most folks here don't find Zurich as interesting as the other cities mentioned.
Check if Mt Pilatus is open in December; Mt Rigi is.
You need more time in Murren, altho there may require minimum number of nights if ski season has opened.
If you're staying in Basel, train to Strasbourg/ Colmar, (about an hour). Strasburg has one of the most incredible Xmas markets, in terms of lights and decorations.
Have a great trip.

Thanks for your suggestions! I'm flying in and out of Zurich. My tentative itinerary is below. Do you think two nights in Murren is not enough? I'm not sure I could switch the reservation this close, but if so, which city would you take out/reduce number of nights there?
So far, the holes in this itinerary are things to do in Basel for just half a day, and 1.5 days open for Zurich.

(Tuesday) Zurich: Arrive at 10:30 AM - Boat ride, Jesuit Church.
Night: Lucerne

(Wednesday) Lucerne: Mt. Pilatus AM, Wall walk, Old church tours, Old bridge tours, shopping, lion monument (walk, free).
Night: Lucerne

(Thursday) Stabbauch falls, toboganning.
Night: Murren

(Friday) paragliding AM, shopping, hike Murren to Allmendhubel (Easy, 1 hr hike).
Night: Murren

(Saturday) Schilthorn AM, St. Beatus Caves if time (19 CHF), Boat ride on Lake Thun 2+ hrs from Interlaken to Thun, Oberhofen Castle, Thun Castle (the boat ride might take too much time).
Night: Bern

(Sunday) Bern botanical garden (free - good bad weather activity), Das Berner Munster Cathedral - Free entrance, spire costs a little (312 steps), Bern bears - hibernating.
Night: Bern

(Monday) Bern Brunch - travel to Basel train station to drop luggage. Day trip to Colmar from 1-5. Basel markets 6:30-8:30.
Night: Basel

(Tuesday) One or two day activities in Basel? Travel from Basel to Zurich. Zurich Christmas markets in evening.
Night: Zurich

(Wednesday) Zurich: Day Activities? Christmas markets in evening.
Night: Zurich

(Thursday) Zurich - Depart 10:40 AM

https://community.ricksteves.com/travel-forum/trip-reports/christmas-markets-switzerland-france-germany-2019

Perhaps my. 2019 Xmas markets trip report will offer some helpful info.

The Zurich main train station has the largest indoor Xmas market in Europe.
Bern has more markets than Basel, which has two main ones.
Leave Zurich for the end of the trip, and go straight to Lucerne from the Zurich airport, it's so easy, 1+ hr direct train.
Have a magical time.

Paragliding is not an option in December, and you will likely need snow boots to hike on the designated winter paths in the Berner Oberland.
I would indeed spend another night in Mürren and just one night in Bern. Bern is beautiful, but in half a day you'll have seen it all.

Do both Colmar and Strasbourg. Colmar is much smaller, and you could do the town in a few hours. Strasbourg is so incredibly beautiful with all the lights, and has maybe a dozen markets spread out across the old town. As a senior woman, I was as thrilled as a five-year old when I first glimpsed the Strasbourg decorations. Can you spend a night? Reduce time in Zurich and Basel?
You'll have a wonderful time!

Pat - I read your 2019 trip report and thank you for the link and the info! I'll be looking into looping in Strasbourg like you suggested.
I haven't booked it yet, but I did find a company (Airtime Paragliding) that is available in the winter. They even have photos on their website of winter rides. I wonder if it's riskier in the winter? I'm already a bit nervous about paragliding, but I think I would regret it if I didn't try it (weather permitting).

Regarding another night in Murren - that location is what I am most excited for so I will look into adding a night. However, I am so worried that poor weather can totally wipe out that destination. I'm 30, traveling with my sister, and very excited to see snowy mountains and will be packing snow gear for this destination. For anyone who has been before, what else is there to do in Murren/what's the town like?

Murren is very small, and outdoor activities are the main entertainments. If you get bad weather in Murren, go to Bern for the day. It's an easy commute and an hour train ride from Interlaken OST.
Have a wonderful time!

Regarding paragliders: it seems that I stand corrected! The only paragliders I see in the French Alps in the winter are wearing skis and it looks a bit more technical, but it does seem that outfitters around Interlaken offer paragliding without skiing in the winter.