Geneva or Lausanne or Montreux? Advice please

If I had to choose one of the three towns you listed, I would choose Lausanne. It's beautiful. It's built on a very steep incline going up from the lake but the views are fantastic. Montreux is OK but I find it to be crowded and noisy and a bit squashed between the lake and the elevated highway that goes around the north side of the lake. Geneva is very nice and I love old part of the city but it's a bit big and impersonal.
Have you considered Vevey? It's between Lausanne and Montreux. It is small, has lots of charm, and is very walkable. There is an idyllic lakefront promenade that you can walk on for quite a distance and the atmosphere is relaxed.
As for which place is more "Swiss", that's in the eye of the beholder I think. If you're looking for alpine chalets you won't really find those on Lake Geneva. You are in the French portion of Switzerland and things tend to look a little more continental European than quaint Swiss. They are gorgeous towns though, all of them!
I would stay in either Lausanne or Vevey for both nights, take a boat to Chateau Chillon the next morning, and then to Lausanne to see the cathedral in the afternoon. It's a steep uphill walk so you might want to consider taking a taxi from the lakeside.

Geneva is a big cosmopolitan city vs smaller more relaxed Montreux. Lausanne is a good compromise. Train to save time; ferry if the weather is nice. I think I would consider a ferry over to the French side rather than visiting Geneva.

You haven't really said what your constraints are as to where you are coming from and going to. What the Swiss call the lakes region is further north, Lac de Neuchâtel and Bielersee/Lac de Bienne.
Geneva is a big city, a nice big city, but not what most people think of as a Swiss experience. Montreux is a big town (or a small city), not a village. Château de Chillon is pretty, but not 'hard core' Switzerland if you only have 2 nights.
If you want a real "Swiss feel", I would recommend getting on a train to Interlaken or Luzern. Train from Geneva to Interlaken takes 2½ hours. You can either overnight there, and continue or take day trips further into the mountains (Lauterbrunnen, Grindelwald, Mürren, ...).
Plan 'B' is to continue to Zermatt, 3½ hours from Geneva.

I agree with Anita, neither my wife nor I really liked Montreux. Chillon is great, but we couldn't wait to leave. And as noted, what people think of as "classic" Swiss isn't generally found around Lake Geneva you need to head east and up into some mountains. The German bits. I'd second Vevey or Lausanne as places to stay.

Rick doesn't think that tourists come to Switzerland to see big cities like Geneva, so it doesn't make the cut to be recommended in his book. His description of Montreux as an "expensive resort" also indicates that it's not the best place to find budget options or low-key cuteness.

Laura, when I first got my RS Swiss guide I was sure I got a remaindered version. There was no chapter for Geneva!

Thanks for all of the perspectives. Truly appreciated.
We will have spent two nights in Lucerne, two in Interlaken before coming to Lausanne/Vevey area. The two nights we are spending in Interlaken, we hope to include a trip to Bern. You seasoned vets I am sure can suggest the nuggets to concentrate on in Interlaken and Bern. Your tips were invaluable to me.

I was in Switzerland in September and took Anita's advice and stayed in Vevey. I am so glad I did. I recently wrote a report on my trip, which is in the Trip Reports section. You may want to take a look if you are looking for ideas. Please consider Vevey!

jpetty,

"The two nights we are spending in Interlaken, we hope to include a trip to Bern."

During your time in Interlaken, are you planning to spend any time touring the Berner Oberland (Lauterbrunnen Valley)? With only two nights there, I'm not sure I'd bother with a day trip to Bern.

Bern is a small, easily managed city. Follow Rick's suggested walk. Trams are plentiful (and quiet, so keep your eyes open!). The train station has many shopping and dining options.