I'm not 100% sure what a "member of the aristocracy" means in the context of 1850s New York - a New York patroon? An exiled European aristocrat? Just a really rich person in New York?

But...if you are interested in what a well-to-do, prominent New Yorker might build for him or herself circa 1850, maybe take a look at the Martin Van Buren house, which is a National Historic Site managed by the US National Parks Service in Kinderhook, New York. The building was built in 1841 (Van Buren moved to the estate after he left the Presidency) and is in an Italianate style, which was very popular in the period.