The Hudson River City term is composed of two crossword solutions, TROY (4 letters) and ALBANY (6 letters). TROY is a city located in New York's Rensselaer County, on the eastern bank of the Hudson River. It is known for its rich history, having been settled in the late 1700s and incorporated in 1816. ALBANY is the capital of New York State, located on the western bank of the Hudson River. It was founded in 1614 and has been the state capital since 1797.