The Meininger hotel is a good place to stay. Its right in Hamburg near the train station and walking distance to shopping, bars and markets. It has modern facilities, tv, pool, wash room ...prices are around 16 euros in a dorm and for an extra 3/4 euros you can have bfast included...
There are lots of beautiful villages on the outskirts of the city that are quite arty and have loads on such as markets/festivals and historic hot spots! about 7 years ago