You're welcome, all. Here's a picture of the magnificent Baltimore monument to Washington. I do happen to like public monuments, and public statuary in general, and Baltimore has some choice pieces. I lived in the city's Mount Vernon neighborhood (where the Washington Monument is) for some 11 years and could see the monument from my window. And I have long known about the Melville quote. But I should admit that, for the particulars about J. Q. Adams and the origins of the nickname, I resorted to Googling.
Baltimore's nickname "the Monumental City" has nothing to do with the monument in Washington. Rather it refers to Baltimore's own Washington Monument, which was completed in 1829, nearly 20 years before the monument in DC was even begun (the DC monument was not completed until 1884). At the time, the Baltimore monument was celebrated throughout the young country, and Melville even mentions it in Moby Dick, in the chapter "The Masthead", as one of the great columns of the world:
"Great Washington, too, stands high aloft on his towering mainmast in Baltimore, and like one of Hercules' pillars, his column marks that point of human grandeur beyond which few mortals go."
But it was not only this splendid erection, which was not yet finished in 1827 when John Quincy Adams (not his father) visited Baltimore, that inspired the president to give the city this nickname, but also another one: the lovely Battle Monument, which was completed in 1825 and commemorates those who lost their lives in 1814 in the Battle of North Point, in Baltimore's outer harbor, which was where Francis Scott Key saw the rockets' red glare and the bombs bursting in air.