So you want to see the same people all the time, but not interact with them?

Why not go and watch local sports teams? You'll likely find the same crowds of people at them, especially if you go to watch the same team. It'll be a loud environment, but you'll get to feel like part of the crowd without actually having to talk or cheer yourself!

(Of course, I don't like sports so that idea would horrify me!)

Libraries often have people there on the same sort of schedule - and coffee shops. If you start going to the same place on the same day at the same time, you'll likely start to notice regulars.

Find out where some groups meet to do things like tai chi? There are groups that do those activities in parks, if you learn their schedule you can sorta stalk them and go to the park to read near them when they're there.

Do you knit? You could always try joining a knitting group. Or a writing group - just find one that is focused on WRITING in one location as opposed to critiquing each other's work. With a knitting group you could always pass off talking by saying that you like to be around people when you knit, but that you are terrible at talking at the same time because you need to focus.

Are there any community gardens near you? You could always get a place in a community garden and then you'll see the same people who are working in their parts too.