Favorite thing: If you are in Hamburg it would be a shame not visiting a town Lubeck. It takes about 50 minutes to get there by train. Train leaves from Hauptbahnhof every hour. I went there to visit the first German ice and snow sculpture festival and it was really fantastic! Please take a look at my Ice World travelogue!
-Another interesting sightseing point I just tried on the 15.April 2000 is Lüneburg.
You can get there in 30 minutes from Hauptbahnhof and in 5 Minutes walk from the train station of Lüneburg you have a very old nice town. Some houses are built in the 17 th century. Unfortunately I forgot my camera, but I will go there again and next time I will make some pictures.