Hi Sarah -
<<"We're really into visiting/sightseeing old towns">>
The old town in Basel is not so large, and did not leave much of an impression on us when we visited. The Tinguely fountain is surely shut down to avoid freezing. ;-(
Luzern has a nice old town.
Solothurn, as well.
Bern is super, and the arcades make it very good for winter weather.
We don't normally recommend Zürich for tourist visits...too far from the Alps. But, the old towns on both sides of the river are large enough and nice enough to spend time there.
A bit out of the way, but St. Gall is really nice, and includes the Abbey and very special UNESCO World Heritage Abbey library, dating back to the middle ages ( although they are both Baroque.)
<<" and walking in the outdoors.">>
Hard to recommend a place for that in February. Switzerland has an amazing network of marked hiking trails, at all altitudes and all degrees of difficulty.
The problem is figuring out what would be free of snow in the middle of Winter. The Rigi almost certainly will have snow on the trails. I think that the trails that I know, all on top or near the top, would be snow covered or icy. .
Wengen is a ski town in February. Nice scenery, though. Many of us on the forum like the town.
Even the lowest altitudes north of the Alps will have that problem You could avoid it by going all the way to Italian Switzerland.. Locarno, Lugano, but it is long way.
In the high Alps. Quite few trails are groomed for winter hiking or walking...You need boots and a hiking staff.