How much time do you have?
If you have more than just a couple of days I would thoroughly recommend a boat trip on the river Wakenitz, from Moltkebrücke to either Absalonshorst or Rothenhusen (they are both restaurants, and both are very nice). The scenery along the river is just lovely.
To get a good view of the town you should consider going up the tower of St Peter's Church (Petrikirche).
Kartoffelkeller is one of my favourite restaurants in the town centre - and I would have no hesitation going again despite the fact that they were implicated in the e-coli outbreak (not their fault, as we now know).
The local beer is Lück - which disappeared for about 20 years but, much to the delight of the locals, has just been revived