Go low-tech and start printing a small local newspaper.
Pay for it with ads from local businesses, and give it away for free at all those stores. Get your regional Chamber of Commerce to help set you up with connections and sales channels.
We have one of these small little local magazines that prints every two weeks with all the local events and stories and humor. It's free (paid for by ads for local businesses), and delivered in bundles to all the local outfits.
At first, I thought it was a little bit silly to start a print magazine in 2020, but honestly, it's amazing and everyone loves it. I look forward to each new edition. And they become hard to find cause people grab them so quickly!
Huge hit, highly recommend. But remember: it's a huge hit not because it's a print magazine; it's a hit because the execution of the couple that manage it. They're top-notch, and it's a "hobby" for them, not their main jobs.
My neighborhood has a guy who runs a small blog/newsletter. It's pretty good! They do roundups on new businesses, events, schools, talks to the city council rep from time to time, and has a generally positive community vibe.
Because it has an editor (and you could break the work up amongst a few people) you don't have the same problems that listservs have (spam) or nextdoor (gossip and paranoia).
Substack or mailchimp would be fine for v1.
If you don't want to distribute something on paper or cover any costs, this is a fine place to start.
Yes, do this and learn firsthand why all the small-town newspapers are gone. Printing, paper, and distribution is expensive, and nobody will pay enough for print ads anymore to cover the costs.
local newspaper with an online version. You can then use the online version to try to use to hook the people into some alternative online platform for the community (a mailing list, a forum, something more advanced)
Pay for it with ads from local businesses, and give it away for free at all those stores. Get your regional Chamber of Commerce to help set you up with connections and sales channels.