This isn't a full answer, but the New York Public Library has a historical menu collection which they've posted online here. There's a bit of a gap in the 1870s, but they have ones going back to the 1850s. Here's one from a NYC restaurant in 1899. One thing to note --- a lot of the menus are from transatlantic ships, hotels, or fancy banquets instead of everyday restaurants, since people were more likely to hang on to those as a souvenir.