I have spent far too much time trying to figure out where this picture was taken from, but I think I have found it. Contrary to what my almost namesake @mgoldey said, the Astor Hotel spanned 44th to 45th Street, on the west side of Broadway (check Wikipedia). Therefore, the corner of the hotel we are seeing is on 45th St, just exactly where Broadway and 7th Ave are crossing. The sign is clearly across 7th/Broadway, and we are looking at it from the northeast. The question is, how far north?

Here is picture looking south from the NW corner of 47th and 7th (in 1957).

https://i.redd.it/hrebrq1oi9nx.jpg

It clearly shows the looming white billboard where the Viking poster was placed a few months later.

As you can see, there is one column of windows visible on the north side of the Hotel. However, if we cross 7th Ave to the NE corner, there would be more windows visible, but not many - you won't really be able to look down 45th Street It would seem that if we were too far south of 47th the angle wouldn't be right. In Anthony Angel's photo we see three columns of windows, so that seems correct.

So, what was on the NE corner of 47th and 7th in the 1950s? A frankfurter shop.

https://viewing.nyc/media/03429a3fa5eb3fad8e9015d49d33198f/

In that 1951 photo, if you zoom in close you can even see it has an awning - most of the restaurants I found in that area do not.

I haven't found a great picture of that corner, so it's hard to see if other details match, but there aren't really other plausible places on the east side of 7th Ave in the couple of blocks north of 47th St.

Hamburger price just skyrocketed up 20%.

Oh how tempting it is to add cartoon thought bubbles for what each of these people are thinking! Every face has a different point of view. I'll just leave it to your individual imaginations!

next Monday, 12/9. Way to go, Mr. D!

Zooks! There's delicious root beer, ladies with cool sunglasses in front of a Kirk Douglas poster for "The Vikings", and to top it all off, the little girl seems to be checking her cell phone for messages!

I wonder how many people remember the paper cone cups that sat in a metal holder? I drank many a fountain soda and even floats in those conical paper cups (there's a stack and a single on the counter under the gals with sunglasses).

The building in the background appears to be the old Hotel Astor, which was on the west side of Times Square between 45th and 46th Streets (demolished in 1967).

Full-size picture here: https://www.shorpy.com/node/9456

I can't quite figure out the angle, but I think that we are on Seventh Avenue and Broadway, looking south towards 46th Street. But I can't quite wrap my head around it.

If we knew which theater The Mightiest of Men was playing at, we could probably nail this down.

https://www.imdb.com/title/tt0052365/mediaviewer/rm191882496

... Motion Pictures!

The Vikings, mentioned previously, was likely still playing first run at the nearby Astor Theater at 45th and Broadway.

The movie advertised on the right is The Vikings, starring Kirk Douglas, Tony Curtis, and Janet Leigh. Ernest Borgnine played the father of Douglas and Curtis, despite being two months younger than Douglas.

You think, maybe they were on their way to see Kirk Douglas, Tony Curtis, and Janet Leigh in "The Vikings?" It was playing across the street. It premiered in New York City, on June 11, 1958. The lunch counter was surely more of a bargain than those expensive concession stands.

With Kirk Douglas, Ernest Borgnine, Tony Curtis, and Janet Leigh. Directed by Richard Fleischer in 1958, based on a 1951 novel by Edison Marshall. The review in The New York Times included this gem: "The sight of those sleek Viking barges sweeping across the slate gray seas, loaded with bearded, brawny oarsmen, is something exciting to see, particularly in the wide-screen and color that are used very well in this film." Be still my beating heart.

"The Vikings" starring Kirk Douglas, Tony Curtis, Ernest Borgnine and Janet Leigh. 1958.

Although I do wonder why all of the adults (seen and unseen) seem to be studying her so anxiously, the face of the little girl standing beneath the counter overhang is just what I needed to see before sleeping tonight. Our fifth grandchild -- a girl -- is due to be born tomorrow. Something about that long-ago child's tiny face, her blond bangs and dress-up coat, and her fingers clutching that hot dog in a soft bun is so encouraging. Life goes on. And it is delicious.