If you do not want to stay with other HC members, or noone is available, here is what other members suggest.
Intantsleep - a regular backpacker´s hostel located on the corner of Altonaer Straße and Schulterblatt in Hamburg´s trendy quarter ´Sternschanze´
Youth Hostel Stintfang An official youth hostel run by the German Jugendherbergsverband. Its loated very central close to the harbour and the famous Reeperbahn.
Kogge - an affordable rock´n´roll ho(s)tel with a nice bar can be found on Bernhard-Nocht-Straße right in the red light district, within walking distance of most of the city´s clubs and bars
Schanzenstern Nice hotel in the quarter Sternschanze resp. in Altona, which is also a very nice area. They are offering affordable single, double and multi-bed rooms and organic food.
Camping Buchholz - the only campground somewhat close to downtown is on Kieler Straße 374 in Stellingen, take Metrobus #4