I consider downtown Düsseldorf as pretty safe (with the usual attention like in every city regarding pickpockets).

There is not one huge christmas market but the booth are located through several parts of old town. I would consider the one in front of city hall (Rathaus) as the main one but there are also booth located. I am not sure, if it is a nice spot to take pictures though.

If it comes to hotels, there are two IBIS hotels and one Holiday Inn (Ludwig-Erhard-Allee) close the main station with easy access to the underground, another Holiday Inn with at one end of Köningsallee, two NH Hoteles with also either easy access to public transportation or close proximity to Köningsallee.