Choosing between Lausanne and Montreux

you can easily visit Chillon from wherever you are staying, not necessary to be in Montreux, it's right next to a train station.

I believe Lausanne is more of a "city" so more options (seeing, eating, lodging), perhaps it was the weather but I didn't care for Montreux. It only served as the end of the Golden Pass before we caught the TGV from Lausanne.

I agree with Phred. Stay in Lausanne. However, my recollection for Chilion is that from the train you take a bus to the castle. In any case, it's easy and quick. You will want to save some time to wander around the outside of Chillon. The lake with the view of the mountains in the background is lovely.

When two places are so close together, I usually just start delving into accommodations and let that help make the decision.
I wanted to get to Lausanne from Montreux but never made it.
Do look up the Gruyere transport--it was not as easy as I had hoped (a rarity in Switzerland but it happens).

The Port D'Ouchy area of Lausanne is a very lovely area to stay with beautiful views of Lake Geneva. There are several hotels along the promenade area there. You can easily take the train from Lausanne to Montreux to visit the Chillon Castle. The Lavaux Vineyards are a World Heritage site with spectacular views. We stayed in Lausanne and enjoyed it, but if you wish to stay in a smaller town I would choose Vevey over Montreux.

Thank you for all your responses!
Any suggestions on Gruyere? It appears somewhat a little complicated.

We love Montreux and would stay there over Lausanne. Very easy to do the castle, walk the vineyards, get a train up to Gruyère. We consider it an advantage having the train station close.

I am also wondering about getting from Lausanne to Gruyere to tour the cheese factory. Train seems workable, but a lot of changing at different locations. What about an Uber? Any thoughts on that?

Thank you all for your replies! Definitely very helpful.