We will be flying into Geneva and want to visit Lausanne, Chillon, Gruyere, and Montreux for 3 nights then off to Interlaken. Which of Geneva or Lausanne or Montreux would you suggest to stay 3 nights as base? I Lanusanne more affordable than Geneva?
Montreux would be you best choice for the places you want to see. You can even walk to Chillon from there.
The median double room price for a random day in June is $275, while its around $210 in Lausanne and Montreux, so in general Geneva seems more expensive (but has a lot more hotels). I would lean toward Montreux (Smoke On the Water!) or Lausanne. RS opinion: "Geneva is on a lake, and so is Cleveland."
In between Lausanne and Montreux is the small town of Vevey. The former hostel Riviera Lodge is now the Vevey Hotel and Guesthouse, but is still cost-effective.