I am not sure how strict the dress codes of a restaurant in a good hotel would have been. Josh might have a problem getting in. I do remember from the O. Henry short stories that oyster bars appeared frequently, and I remember reading somewhere that they were the equivalent of hamburger stands today, especially in New York City, and that would probably hold for much of the east coast. They were cheap, popular food. They did not become an expensive delicacy until after the 1920s, when the oyster beds around New York City had been wiped out by pollution and too much harvesting. I think steak and lobster would be the expensive items on the menu. In doing the web research I found out about "lobster palaces", which would be less sedate than the hotel's restaurant, and an atmospheric setting if Josh stays in 1914.
Local prohibition laws by this time made it difficult to get a legal drink, but national prohibition did not get enacted until 1919. And a popular staple of today, caffeinated cola, was under legal attack from the government. It spawned one of the more memorably-named court cases, "The United States vs. Forty Barrels and Twenty Kegs of Coca-Cola."
I thought that Josh might also have had a problem with shaving, but the safety razor was invented earlier than I thought, and would be available to him.
Scattered thoughts on the Time Traveler (1914)
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