Not comprehensive...just a quick sampling ...
Cafe Pick Me Up
Odessa
Ray's
7A
Native Bean
Yaffa Cafe
Starbucks (Second Avenue and Ninth Street)
Veselka
Roastown Coffee
Ray's Pizza/Bagels
7-Eleven!
Gemma at the Bowery Hotel, for something more fancy
Everyman Espresso, 13th Street
The Bean
Pinisi Cafe/Bakery (East Fourth Street neat First Avenue)
Casa Adela (Avenue C near Fifth Street)
What else have you seen open this morning...?