Corner of Allen and Elmwood
all damned night!
The Towne is an obligatory stop if you've made it to Buffalo's closing time (4am). They're one of the best greek restaurants in Buffalo and they're conveniently near several drinking, err, entertainment districts.
You can get anything on their menu, so you're not limited to breakfast. Usually plenty of tables at that time; the breakfast crowd doesn't show up for another two hours.