The longest night for you would be for which midnight is closest to the exact moment of the winter solstice. Think of it this way:
The winter solstice moment is when Earth's polar axis for your hemisphere is tilted farthest away from the sun. The longitude at which it is local midnight will experience the absolute longest period of night symmetrically around that point. For example, say that ##°W longitude happens to be the longitude that is directly opposite the sun at the winter solstice moment. For people north of the equator on the ##°W longitude line, their night will be the longest it can be.
If you're a little east of that line (you'll get daybreak slightly earlier), then your nighttime will be VERY slightly shorter. If you're a little west of that line (you'll get daybreak slightly later), then your nighttime will also be VERY slightly shorter because you did not have your local midnight at the time of the winter solstice.
If you go farther from that line of longitude, then while the night you had closest to that midnight point for ##°W will be the longest for you of the year, it won't quite be as long as it would have been if you were at ##°W longitude.
So if we take this and go back to your actual question, the winter solstice was on Dec. 22 at 05:30 AM UTC in 2011 for the northern hemisphere. Greenwich is defined as 0° E/W longitude, and there are 15° longitude per hour. So we need to go back into night (west) by 15°x5.5 hours = 82.5° W longitude (somewhere in the western US/Canada). They experienced the absolute longest night Dec. 21/22. People 82.5°W and ±90° of them would also get their longest night Dec. 21/22. People 97.5°E (opposite side of the planet) and ±90° of them would get their longest night Dec. 22/23.