This is for people that I live with.
I don’t mean any lame team building exercises, but casual group activities. It could be something mundane like organizing a trip to the store together. Movie trips would also be fine as would showing something on the home projector, though I feel like there’d be more distractions and temptation at home.
One important point I have not found in the comments is the schedule. If you schedule such an event, stick to it. Don’t move it around in time or location, especially not last minute. My son had serious problems when they moved tests in school e.g. from 08:00 to 10:00.
With repeated schedules, avoid fixing them to e.g. “the second Wednesday in the month”. If that second Wednesday happens to be a public holiday, you might be in for a surprise, Better: “The date and time for the monthly activity will be published at the beginning of the month”, and make dead sure the paper is always on the notice board just before the first.