Βράδυ is another word for night.
Supposedly, there is a difference between βράδυ and νύχτα. Βράδυ is the time of the day that starts right after sunset, lasts for a few hours and it is then followed by νύχτα. However, the difference is not that big of a deal. Most Greeks use both words. ^.^
They are both correct, as mentioned above, but νύκτα is less commonly used nowadays (it is basically an older form). There are further similar cases with κτ/χτ, in most of which the "χ" form is more common in everyday language, such as δίκτυ/δίχτυ (net), κτυπώ/χτυπώ (hit, knock), but it depends on the word and the context. A more general rule is that the "κτ" forms are more formal.
I was offered "Σημερα τα νυχτα" as a possible translation; "Today the night?" Fortunately it was the only reasonable option.