Call
They should be able to check with coat check.
Call the theater and ask. They check all bags at entrance and I'm not sure how they would react to big bag.
I would call the theater and ask them what there rules are I would think it would be okay but would ask before you go.
Have your meal at Sardi's and leave it in the coat room. Pick it up after the show. I've done this many times. It's 2 doors down from the theatre.
I would imagine you can but I would call to be sure
I have no idea I think you'll have to call them on that one
I never thought to ask but Ive never seen soneone do it since they check the bags before entry in the bldg.
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