Several well known fast food restaurants in the train station itself open early (McDonald's - 04:30) or are open 24/7 (Springtime).
If you're after a bar, Oktoberfest is a well known one that is open until 05:00, and nearby Bound closes at 06:00. However be aware that they are not close to the train station.
Realistically your best options are in the Old Town, but most bars are closed by 02:00, so you'll need to look hard on Google Maps. I wouldn't recommend trying or exploring the area outside the train station, because it's not a particularly good one.