Some suggestions for an accommodation nearby the DESY premises.
Official DESY Hostel.
The Mercure Hotel am Volkspark.
This is the hotel formerly known as Novotel Hamburg Arena, locatetd at 2 min. walking distance from the DESY secondary entrance at Luruper Chaussee (which is the closest to the CFEL building).
The Hotel Schmidt.
This hotel is located very close the S-Bahn station and bus stop of Othmarschen. It is at 20 min walking distance from the DESY main gate, or 10 min. by bus (a number 1 will take you directely to the DESY main gate).
The B&B Hotel Hamburg-Altona.
A cheaper solution with respect to the hotels suggested above, and at 10 min. bus ride from DESY (take a number 3 until Trabrennbahn Bahrenfeld and then walk 5 min. to the DESY Side Gate of Luruper Chaussee).