These are open this morning and probably have been for a little while.
331 Henry St.
M-F 5am-5pm, Sat 5am-3pm, Sun 5am-12pm
A tiny luncheonette squeezed in between the deli and the café (below). Counter with stools but mostly for takeout. Breakfast, sandwiches & burgers. They'll probably get much of their business from Long Island College Hospital.
Jam for Bread Café
333 Henry St.
M-F 6:30am-8pm, Sat 9am-10pm, Sun 10am-5pm
I'd originally called it Sam for Bread, but someone here interpreted the saxophone in place of the first letter as a J and that's surely right. I've only looked in the window; looks like a cafe with small round tables and chairs. No menu posted in the window so I don't know anything more about it.