It’s a shame that you only have six days in NY, I have been lucky enough to of been to NY twice and have spent a total of 13 days there. It is a city that doesn’t sleep.
With your “Holy Grail” of B&H just be careful of the stores opening hours as they are not the normal hours you would expect as it is a Jewish run business and they observe Jewish holidays and hours i.e. they close at 1pm on Friday and don’t reopen to Sunday. But it is a cool store to wonder around.
I would recommend the Staten Island Ferry (what is free and runs every 30 minutes I think) as its takes you nice and close to the Statue of Liberty …I have been to the Statue and Ellis Island and with security & queuing to get on the boat its taking about 2 hours just to get over there …its took us a full day to do this and I thought that the drive by of the Staten Island ferry was just as good.
Time Square is just a tourist trap but go and looks at the lights and go to Toy’s R Us. A couple of blocks to the west is FAO Schwarz toy store what is the home of the giant piano from the Big Movie …it was fun to play on. Also outside this is the Apple Store and the start of Central Park ...the park is worth looking around with its ponds, Strawberry Field (Lennon house is just across the road from here) and some great mosaic tiles in some of the archway you walk through.
I would recommend the 9/11 memorial museum; it was very moving. Make sure you book your tickets online as you book a time slot.
I have been up both the Empire State Building and the Rockefeller Building (One trade was just being finished when I was last there in 2014 and this in on my list of things to do when I go back in 2018). I thought that the views were better from the Rockefeller Building as it more in central Manhattan but enjoyed the nostalgia of the Empire State Building. Book your tickets online …with the Empire State Building its means avoiding one queue and just having to worry about security while in Rockefeller you book a time slot for the elevator.
Walk the Brooklyn Bridge …it was on my list of things to do in 2014 but I tore a tendon in my knee just before leaving and was on crouches …I know a few people who have and they loved it.
As for shopping, let your wife hit Macey’s ….it takes up and entire block and you just can’t comprehend the size of the store ….it also had the best free wifi (had no issues with Video skyping from here) …also you can go to the information booth/center in the store and show some overseas ID and get a 10% discount voucher. Looking at some of the shops on 5th Avenue was fun …. we brought something just to say we shopped on 5th Avenue.
As for food I always had nice service and food with the exception of TGI Fridays in Time Square and the Hots dogs from the stands are great.
Overall for me I just enjoyed walking the streets (I have never felt so safe walking around a city) and taking in the atmosphere of this great city as it never sleeps …I am jealous and have now start my countdown to 2018.