As Hamburg is the second largest town in Germany there are so many ways to spend a few days at leasure - it really depends on your interests:

That´s a good one. Lübeck has a very nice old town area, nice beaches (depends on weather) and of course the famous Marzipan.

Not only one. As you´re too early to enjoy the beachclubs, I recommend the Au Quai in "Große Elbstraße", the IndoChine in "Neumühlen" or the rooftop bar in the hotel "Hafen Hamburg" for a classic drink with unbeatable harbour views. In Große Elbstraße are also many good restaurants in different styles.

Many other things to do:

- hop on hop off city tour for first orientation
- harbor cruise
- alster lake cruise
- walk through "speicherstadt" (the old freeport) and new and stylish port city area
- walk through "Blankenese", Hamburgs little Italy when you have good weather.
- visit one of the many museums like "Hamburg History Museum", "Art Hall", "Spice Museum" and so on.
- from end of March (22nd) to middle of April there is "DOM" in Hamburg - big party and action park on "Heiligengeistfeld".
- there are many musicals in the city
- nice side trip destinations by train or car are Lüneburg (old town), Bremen (more or less like Hamburg - only smaller) and as mentioned above Lübeck.
- if you´re a firsttimer in Germany consider a day trip to the capital Berlin. Highspeed-Trains are running every hour - traveltime is 90 minutes.

For an overview and an event-calendar: main tourist information is in the central station.

If you´re not familiar with the surroundings, don´t enter the reeperbahn district by night alone. It´s not really dangerous but can be an expensive experiance - afterwards you will know the northgerman word "kobern" very well ;-) - better join an organized tour or ask the concierce at your hotel.

http://www.hamburg.de is availlable in english and gives you many more suggestions.