In "Goodbye to the Marketplace: Food and Exclusivity in Nineteenth-Century New York," Anne Mendelsson writes about imported produce a bit. It started appearing in New York (mostly from the Caribbean) in the late eighteenth century, though quality was poor. The point wasn't that asparagus, or Bermuda peas, would taste any good, but they were status symbols, a form of conspicuous consumption. Most of the produce eaten by most people (and all of it by ordinary people) would have been relatively local, ie shipped from the surrounding counties and states. The Erie Canal was the first means of shipping Midwestern grain to New York, though grain is not quite the same as lettuce. It would take until the invention of refrigerated railroad cars for larger quantities of perishable goods to reach New York from far away.

That's not the most complete answer, but it's part of the puzzle. The essay can be found in this book:

Beckert, Sven and Julia B. Rosenbaum. The American Bourgeoisie: Distinction and Identity in the Nineteenth Century. New York: Palgrave MacMillan, 2010.