No problem. There is quite a selection for dining after midnight:
1. A Würstelstand: dozens of kiosks all over town are selling hot sausages, or kebap, or fried noodles...
2. Motto: Motto am Fluss and the original Motto on Schönbrunnerstrasse are traditional spots of late dining. Open until 2 a.m., on weekends until 4 a.m.
3. Cafe Drechsler: this Kaffeehaus on Naschmarkt used to be the watering hole of the wholesale merchants delivering the food for the market. Times are changing, but Cafe Drechsler is still there: Open 23 hours a day, 3 a.m. to 2 a.m, only sunday they close between midnight an 8 a.m.
4. Cafe Europa, another overnight cafe, opens 9 a.m., closes 5 a.m.
5. Livingstone.: A colonial style bar and restaurant, open every day until 2 a.m., great steaks