A brownstone is a town house with a front made of brownstone. Sometimes it’s used to describe all townhouses generically. Some have solid brownstone fronts, the most valuable. Some have brownstone elements on the facade. Others are made of other materials entirely.
There are lots of brownstones in Manhattan. You can see them in the West Greenwich Village, Gramercy Park, the East Side, Upper East Side and Upper West Side.
They are brownstones elsewhere in Manhattan, including Harlem and the Upper Upper West Side going all the way up to the Bronx. There are miles of them in Brooklyn.
Probably the best place to see them is to going to Central Park West at 59th Street and start walking north. Take any side street going east and walk for a few blocks to around Third Avenue, turn left (north), go a block, and turn left back and walk west toward Central Park. Then turn right heading north and repeat.
If you ever go through Middletown, Conn. There is a quarry by the Arrigoni bridge that supplied all the Brownstone for New York City. You can go into the quarry and explore it, very interesting history.