I'm in Seattle, which you would expect to be a pretty popular spot for independently run cinemas, but my local (a 4-auditorium theater) is teetering on the edge of closing due to high rent and low attendance. I saw Inside Out 2 there on a weekend evening and the entire house only had only about a dozen people in it.
Meanwhile, a few blocks down the street, a tiny independent cinema with one auditorium that seats ~70 and generally only runs older and niche films seems to be doing kinda-ok.
The cinema marketplace is changing really fast compared to even 10 years ago and there are sadly going to be some casualties.
Ultimately i think we're going to get back to movie houses with one to three auditoriums, and with a wide range of uses: movies, streamed live performances, television premieres and finales, away-game playoff sports, as well as a healthy usage as rental space for public meetings for reasonable rates.
We have some pretty popular independent movie theaters here, too. Cinerama (or whatever they changed the name to), Central Cinema, I'm sure there are others.
Cinerama was purchased by SIFF (now dreadfully renamed "SIFF Cinema Downtown"), which is basically a local chain now (along with SIFF Cinema Uptown, SIFF Cinema Egyptian and the SIFF Film Center).
As for true independents around here, you've got the Grand Illusion, the Beacon, the Ark Lodge, Northwest Film Forum and, of course, the Majestic Bay up in Ballard.