Basel?

Basel does not have a lake or mountains like Luzern. It is a bigger city. It does have a river, a lot of museums and a lovely medieval centre to wander around. It is very photogenic (click here).
Basel's official tourist website is: https://www.basel.com/en

It is also a good base for the southern Black Forest, and southern Alsace. Colmar an Strasbourg are easy day trips by train, as is Luzern, Bern etc.

Chris F has hit on some of the highlights - he would as he lives there - but from one who doesn't, I love Basel. I went from 15 years of driving straight through and hating the traffic to getting out of the car and looking around and loving what I found. The city very much has its own vibe - different than other parts of Switzerland and different than the nearby parts of France and Germany.

It is a very cool place.

Basel couldn't look less impressive as you drive through on the Autobahn, and for that reason, I never felt compelled to stop. But then once I stayed there overnight on the way to Zermatt... and I saw what I was missing from the road. A very pleasant, walkable, livable city, if not exactly Europe's most spectacular. As the others noted, though, you won't see the Alps in Basel. The lower Swiss Jura mountains surround the outside of the city and block the view of the more distant Alps. The southern portion of the Black Forest is just to the north over the border in Germany, as well as one of Germany's best wine regions.

Overall, I would probably chose Luzern as a base, but I wouldn't avoid Basel either.

Basel is one of my favourite cities in Switzerland, not for the reason other have stated, but for the people. The people from Basel are always helpful, friendly and a whole lot of fun.