I wouldn't worry about bedbugs at AMC Empire, I've been there a ton of times and never had an issue. I'd also suggest going to their Dolby Cinema screen; it's got state-of-the-art projection and sound, a massive screen, and big leather reclining seats.
AMC Lincoln Square is also great, and has one of the biggest IMAX screens out there. The seats are standard movie chairs though, as opposed to the big recliners. If you're planning on going to dinner before/after, I'd probably go with Lincoln Square since you can find legitimate food options, not flyover strip mall fare like TGI Fridays and Olive Garden.
The AMC on 84th street, and the one at Kips Bay, also have big reclining seats, but standard screens.
Outside of that, find whatever's convenient for you.
Lincoln square 13 has it playing in the big IMAX screen so I would go there.
If you want an IMAX theater do linconln square. If you want the best experience outside of IMAX do AMC Empire Dolby Cinema.
If you do IMAX get a seat in last 3 rows. If you're doing Dolby cinema Row C, D, and E are best. There is a large gap between the screen and row A. So don't go by the diagram on the website. You're not actaully that close to the screen in rows C, D, and E.
Keep in mind this is not a legit IMAX movie. Not filmed with IMAX cameras. IMAX is only really worth it if they used IMAX cameras IMO. I'm a bit a snob when it comes to theaters and I'm seeing this movie at AMC Empire.
The Alamo Drafthouse Brooklyn still has showtimes on Fandango...
Back when I visited New York in 2014, I saw Guardians of the Galaxy opening night at the Ziegfeld theatre. I would've recommended that to you but I just read that it closed down to become a ballroom :(
I would recommend the Battery Park Regal. Super comfy *recliner seats, not too busy and in a nice area.
Some great indie theaters are Angelika and IFC Center. Don't know whether they will be playing Black Panther, but they are in the East Village and there are cool bars/restaurants nearby.
Despite the comments below, the AMC theater at West 84th Street has some great screens and you will then be in the Upper West side, close to Natural History museum, Lincoln Center, and Central Park.
Regal Battery Park is a great theater. There's a selection of restaurants right by it, and a nearby shopping plaza if you're looking to kill time. Seats recline and are super comfy.
Idk they're all kind of nasty.