Is it possible to create "local digital" experiences?
Frankly, I make sure to make references to the real world local.... a physical place.
Also, I think you are halfway to acheiving a "local" feel if you are concentrated or 'niche' in some other way.
For instance, I know a site that caters only to giving chefs an insulated community... to experiment, share insights, challenge each other, even foster some friendly competition that tends to light up their creativity -- which can sometimes falter if you are dealing with a very limited menu that doesn't change in your for a living gig.
That community has a local feel. Even though chefs are from all over America, and even the world! The "local" for them is the experience of the envirnoment found in working kitchens... or even the particular particulars around one kind of cuisine.
the point is that people are coming together to engage in exchanges around specialized knowledge in a way that new- adopters simply cannot do. Sometimes that information is about having lived in or grown up in a particular 0place. Sometimes it's about attending a particular school. And sometimes its around a particular microcosm of culture - and they know what each other means when they speak. Saying "Friday" to some people means something very different than it does to the rest of the country.