Originally Posted by USAFAN
True - the Hauptbahnhof (Central Train Station) is not far. The area toward Lake Alster is safe. However, the area "behind" the hotel (Sankt Georg) is not; it's worst than the St. Pauli red-light district. However, the walk to the station is OK, when you go near Alster towards Hotel Atlantic, and then left (I believe it's Holzdamm) to the station. Don't go to Georgs-Platz at night.
Have a great time in Hamburg & Berlin.
USAFAN's advice, as always, is spot-on. Here's a link to a map of the area at the back of the Hbf:
http://www.google.com/maphp?hl=en&q=...,0.022702&om=1
Use the zoom-in feature at the upper left of the map to see the exact route that USAFAN has specified (if you take the Jasper bus from the airport, it will drop you at the back of the Hbf, in the "driveway" area of Kirchenalee that is clearly visible on the map