Promenade between Ouchy (Lausanne) and Chateau de Chillon

That is quite a long distance,I have walked Ouchy in Lausanne,very nice and waterfront in Montreux also very nice,didn't walk the Chateau only toured it.
Mike

The promenade in Vevey from the main square where they hold their weekly market, going east along the lakefront is my favorite! There are several large, beautiful, old hotels if you want to splurge on lunch or dinner, a couple of interesting and small museums (the museum of food and another one about toys), some nice sculptures, gorgeous trees, and benches to sit and enjoy the views over the lake and the French Alps on the other side.

Ouchy (Lausanne) and Chateau de Chillon

That is a very long walk, not suitable for a day trip. It is 30 km and will take over 6 hours nonstop each way to walk.

I've visited the chateau several times ( always from the outside never inside ) by train and car, including by train from Lausanne, but walking there never occurred to me. I think it would be rather fun to arrive by boat.

The premier real estate is along the lake, so it's really all beautiful. Since you are walking, I would probably opt for Ouchy, Lutry, Pully, Cully, Vevey, La Tour-de-Peilz, Clarens, Montreux, Territet.

stick to Montreux to the castle

Here's my ideal way:

Take the boat across Lake Geneva to Chillon castle. This gives you a unique view of the castle. Looks like it's floating. Tour the castle. Walk to Montreaux along lovely lakeside path dotted with perfectly maintained flower plantings. I believe the walk was about 2 miles. Have lunch or drinks at a lakeside cafe. Take train back to Lausanne (short trip). Great day outing.

We also did the walk from Lausanne to Lutry and took a bus back. Nice but not as good as above walk.