There are plenty of hotels and private B&B in and around Dessau. Enquire with Tourist Information.
cheap
Youth Hostel, Ebertallee 151, 20 minutes walk from the main station. Prices for B&B start at 18,50 Euro.
Bauhaus, Gropiusallee 38. Ever stayed in a world cultural site ? You can at the Bauhaus dormitory. Single B&B 20 Euro, double 35-40 Euro. Simple standard, shared bathrooms.
$$$
Top end
NH Dessau, Zerbster Strasse 29 city centre. 4 star business hotel, Prices start at 80 Euro single B&B, 100 Euro double B&B.
Radisson Blu Fürst Leopold, Friedensplatz 1 near station and city centre, 4 star business hotel, Prices start at 80 Euro single, 100 Euro double room only.