I hope you will appreciate the Morgenstraich. I prefer to sleep in the AM, but, then, I'm a lot older than you are. ;-(
In Basel, try to see the Tinguely water sculpture. Might be frozen...don't know if it runs in the winter.
Basel has some great art museums. Any interest?
February is not a great time for walks or hikes.
However, the lake shore on both sides, (especially northeast side) in Zürich and Luzern ( east side) might work for you. Both have nearby tram/bus access along the way. Otherwise. look for short walks wherever you are staying.
The Glacier Express will work, as Annika noted,...but you have to go to and from the start and finish. That will take a big chunk out of your available time. Although there is a winter break in the GEx schedule (not sure when that is) other "regular" trains take the same route.
If I were doing it, in February, I would not go so far afield as Zermatt and St. Moritz. Although, if you are not jet-lagged from an overnight flight from the USA, it would be easier for you, than for me when I arrive with inadequate sleep and 6 time zones change.
Nonetheless, I'd go from Geneva to Luzern and spend a day or two there and in the surroundings. lake, mountains, nice old town...
You could go from Geneva to Luzern after you arrive,easily, using the fast route via Zofingen, near Olten. or, you could go to Montreux, stay over, and take the slower scenic Golden Pass route/train to Luzern on the next day. It passes by Interlaken.
Check the timetable -
When you are finished in Luzern, about one hour train ride to Basel from Luzern.