I did a search online but couldn't find an accurate list. Anybody know of a list by neighbourhood that is up-to-date?
According to the Starbucks official website, there are two Starbucks locations close to West Village that fulfill your requirements
Lafayette & 8th Street
13-25 Astor Place
Open 5:30 AM to 1:00 AM
New York University
45 West 4th Street
Open 7:00 AM to 12:00 AM
Starbucks store allocater may help you.
It can show every single Starbucks location, opening time, plus some extra service like wifi/mbile payment/24-hours opening, on Earth.
However, many Starbucks stops selling around half hour before closed.
Looks like there's one, according to Yelp.