What do you call the directions orthogonal to uptown/downtown in Manhattan?
The orthogonal travel to uptown/downtown in Manhattan is crosstown.
Yes, I know that u/d is binary and crosstown is not. New Yorkers ususally know where they presently are. If they are West of Fifth Avenue and say they are going crosstown, they are going East. Ditto on East of Fifth.
When current location cannot serve as the indicator or more precision is sought, a New Yorker would probably say to the East Side or to the West Side. If you were on the West Side (say 9th Avenue) and were only going a few blocks east, (say to 7th), you might say go east to 7th. Probably the direction would not be mentioned, except to a non-native, since NYers know !st is east and 12th is west.
Perhaps more commonly, New Yorkers talk about the neighborhoods to which they are heading, rather than the direction itself. For example, in Manhattan alone we have
- the East Village
- the West Village
- SoHo
- NoHo
- Tribeca
- Midtown (sometimes Midtown East or Midtown West)
- the Upper West Side
- the Upper Upper West side
- the Upper East Side
- Turtle Bay
- Chinatown
- Little Italy
- Harlem
- East Harlem
- Morningside Heights
- Riverside
- Yorkville
- Sutton Place
- Chelsea
- the Flatiron District
- the Garment District
- the Theater District
- Battery Park
- Wall Street
- South Ferry
- [and many, many more]