Wife's birthday weekend and already have tramlines tickets so am a bit gutted to not be able to go.
Have actually been to Lubeck twice, the Holstentor is a must see and it's not far from the train station. Train to Lubeck is about an hour tops, and it's not a crappy Northern Rail pacer train either... Lubeck is popular in Germany for it's Marzipan, and there are dozens of shops devoted to the stuff.
Beer should be relatively cheap up there, and if you're in Hamburg, and you do happen to visit the Reeperbahn, you can drink on the street there, so grab yourself a bottle of Astra at one end, and get ready to 'enjoy' the sights. Club Molotow is at one end and frequently has live bands on from UK/America.