I understand the draw to Luzern from photos. It does have a very lovely historic center. What I don't love about it are the crowds. It's so crowded. You could get to the Geneva airport from Luzern for a noon flight, but you'd need to leave by 6 am, as it's a 3 hr 15 minute journey. If you really, really want Luzern, have you looked into changing your flight to depart from Zurich? If Montreux isn't exciting to you, then with the places you have on your list, Zurich would be the better entry/exit point. With airlines these days, if there is an available flight you should be able to change. If you were able to switch to atleast one leg in or out of Zurich, then Luzern would be an easy choice, as it's only a 1 hour direct train to the Zurich airport. No where but Montreux is convenient to Geneva. Even Wengen is closer to Zurich.
If you can't change your flights, then my advice for 8 nights is to stick to 2 regions of Switzerland, which kind of confines you a bit in my mind to including Montreux since Geneva is your entry/exit point. The more time you spend traveling long distances, the less time you have to actually enjoy. I'm giving you suggestions based on my experiences and how I would do it. If it were me, I'd be going to Wengen the whole time and then 1 night in Montreux, but I'm not a city person and once you experience the mountains in Switzerland most people never want to leave. I didn't, which is why I live there 3 months out of every year :) Maybe I'm a little over biased, ha!
But back to the main question of Bern vs Luzern vs Montreux.
Bern
pros - least touristy option, old historic charm, great convenience to Wengen to maximize your mountain time
cons - maybe the least tourist highlight reel options?
Luzern
pros - old historic charm, social media highlight vibes, lake
cons - most touristy option, least convenient to the rest of your itinerary
Montreux
pros - experience the French part of Switzerland, which will be unique to your itinerary, Chateau de Chillon is my favorite castle in all of Europe, very convenient for your itinerary, lake
cons - less quaint