How do I achieve this shape?

Sorry the title is crappy, I can’t describe what I’m doing with words. I need to take this cylindrical object:

and cut a piece out of it (or move the vertices) like this:

Is there any way to do this without moving one or just a few vertices at a time? That would drive me nuts.

proportional edit

or booleans

… proportional edit will result in a much cleaner mesh, but you don’t have as much control over the shape of the indentation

Good enough.