My initial impulse would be to take the Jackson and renovate it. (This is all, of course, assuming money is not an issue.) That place has many of the elements I would want in a movie theater: it's small (three screens), it's easily accessible to public transportation, it has an old-fashioned marquee where one can see everything that's playing at a glance. I wonder, however, whether or not it's too small. I might prefer something more like the Drexel - a stylish Art Deco look, with a few more screens, plus the adjoining cafe next door. (The Jackson did recently acquire new owners, and this post is not meant as a knock to them.)
A combination of the two, then, assuming this theoretical theater will be in Queens. Jackson Heights would be a good place to base it - centrally located within the borough, lots of buses and trains all around, plenty of commercial business - but Astoria would put it much closer to Manhattan, not to mention the proximity to the Museum of the Moving Image. Not sure which neighborhood I'd go with.
If I were to stick with Jackson Heights, I'd try to make it more like the Drexel. Three screens is fine, at least in the beginning. If it were possible, I'd try to find a way to have a connected cafe next door that serves Spanish and Indian foods, in addition to traditional coffee shop fare, as a means of catering to the local cultures that dominate the neighborhood. Like the Drexel, one could walk to this cafe from inside the theater after seeing the movie. It would have free WiFi, of course, and would be decorated with movie-related art and movie posters from around the world.
In my advertising, I would place a heavy emphasis on using public transportation to get to the theater. The Drexel has a small parking lot in the back, which is the best place to put a parking lot in a neighborhood like Bexley, where only one city bus goes to the theater and there's no subway. JH is much more dense, and the 7 train literally drops you off within a single block of the theater. I would naturally put a bike rack on the sidewalk in front, just like the Drexel.
One of the most appealing aspects of the Jackson is how the center auditorium is done up very fancily, like that of an old movie palace, with decorative columns, carpeting, a chandelier, the works. (The other two screening rooms are plainer.) I would keep this as is, and I might even sell it a little bit further by giving it a name (not sure what - I'd probably name it after a director or actor) and laying out a bright red carpet from the entrance to the box office.
No matter which neighborhood this theater would be in, I'd follow the example set by Tim League and the Alamo Drafthouse in terms of controlling audience behavior, which means I'd have ushers on staff. I probably wouldn't need more than two, maybe three, for evening shows and weekends only, but they'd be there, and I'd fully empower them to deal with cellphone talkers and mothers with crying babies and rowdy teenagers the same way the Alamo does - and I'd be completely upfront about it with the customers.
As far as programming goes, I'd do my best to provide a wide variety of material, Hollywood and independent, foreign and domestic, classics and new stuff. At least half of my films would have to be the high-profile Hollywood new releases because duh, they're moneymakers. I'd try to get a sense of what the customers like and cater to that as much as possible, but at the same time I wouldn't be afraid to share my personal tastes with them as well. I'd host film festivals and midnight movies, naturally, and I'd attract local filmmakers to premiere their movies at my theater, but I'd also try to educate the audiences on film in general: what constitutes a good movie, and what movies from the past can teach us today. To that end, I'd have a kind of critic-in-residence program, where every month a local film reviewer or blogger would program a few movies of his or her choosing and have a Q-and-A afterwards to talk about them.
I'd also try to work with the local businesses and get some cross-promotional stuff going on. If a new release can be tied in some way to a neighborhood store or restaurant, I might find a way to use it as an opportunity to promote that business. For instance, if people were to see Captain America and there was a comic book shop in the area, they could take their used ticket stub to the shop and save ten percent on their next purchase of a graphic novel. Something along those lines, with an emphasis on local, neighborhood businesses whenever possible.
Most of all, I would foster an atmosphere of fun and good times for everybody who comes. I'd get to know my audience personally so we can share ideas on film. And I'd constantly try new stuff to not only see what works, but to keep things lively. Would you go to such a theater?