Hilton Garden Inn (45 East 33rd St) has a bathroom on the first floor. Just enter and you’ll see the front desk on your left, walk past them and keep going straight and you’ll see the bathroom on your left. They have only two stalls. This bathroom also has music being played so you can take a nice dump with plenty of privacy.
Lotte New York Palace has free umbrellas at the main entrance (East 50th Street). The bathroom on the second floor is a bit crowded so take the elevator to the 5th floor. Nobody uses the bathroom here. lol.