Zurich or Geneva

Neither, Luzern. If you are flying home after Zermatt, you can get a direct train to Zurich airport in about 70 minutes.

Ditto, I loved Lucerne--but it would also depend on the flight choices. I would not necessarily stay in Geneva, but other towns on the lake are quite nice (Montreux, Lausanne, Vevey) and it's easy to get to Geneva airport from them.

Should have added that we are flying to Athens next so ease of this needs to be considered. Thanks!

Indeed, search the outgoing flight availability, though I think they are probably fairly similar, one never knows.

There are trains from Luzern to the Zurich airport rail station, a bit over 1 hour. Zurich and Geneva are both OK, but Luzern is better.

Between the two, I would favor Zürich because it IS more walkable. You can take a nice walk along Bonhofstrasse down to the lake and another through the Old Town area. RS has a nice walking tour of Zürich in the Switzerland Guide. Depending on your time and what you’d like to see, could you spend a day and a half in Lucerne and half a day in Zürich?

If you can fly out of Geneva, I actually suggest to consider Lausanne. The train connecting Zermatt to Geneva stops there and you can get a full and better understanding of the Swiss. Your stay is mostly concentrated in the Swiss German side of Switzerland while Lausanne is in the heart of Romandie (the French side). You can take a train and visit Vevey and Montreux easily (lots of famous people lived or visited this area - starting from Lord Byron and ending with Charlie Chaplin and Freddie Mercury). The UNESCO Lavaux wine region is right between Lausanne and Vevey, while Chillon Castle - the most visited Swiss castle - is at a stone's throw from Montreux.
The Geneva Lake is unlike any other Swiss lakes, it is so grandiose and impressive that you'd think it's a sea not a lake. The climate is mediterranean and there are so many tropical plants and trees.
After living in the French region for almost 2 years, I can say without a doubt that Switzerland is much more than the moutainous central and eastern German speaking regions. The French and the German Swiss cantons are so different that one cannot say they fully got a grasp of this unique European nation. Not to mention, that there is an Italian canton, Ticino, which would actually complete the Swiss experience, but to include it one has to have at least 10 days in Switzerland.

Safe travels and enjoy your Swiss adventures!

I think Zurich has a denser base of attractions, and is more walkable. It's unclear if you actually want to go hiking, or if you mean simply independent tourism in a big city. Zurich also has nice nearby attractions, if you want to skip downtown, like the Rheinfall and Stein am Rhein. I suspect month of year may make some difference, but it's not like I go to Switzerland a lot.

Thanks for all the advice. Tim we will have just finished a hiking trip so your advice about Zurich is helpful.