@miles What I used when looking for my place where :
- https://www.immowelt.de
- https://www.immobilienscout24.de/
- https://www.kleinanzeigen.de/s-wohnung-mieten/

One nonsense thing the German can be a pain with a their credit score (Schufa report). I have been able to get one (that stated that Schufa knew nothing about me for a reasonable fee, but it clearly is a pain, and in the end was probably not that useful).

You probably want to get someone from around Düsseldorf to tell you about the good / bad neighbourhood.

Another annoying thing to account for, is that as soon as you have moved in your house, you'll need to register with the local city office your address (and that has to be done in person if you come from abroad). (Anmeldung).

They'll also ask for your religious affiliation (for tithe purposes, if you happen to be a member of one religion that gets the Church tax. There have been occurrences of people baptised in the Catholic church getting caught after the fact and having to pay up a lot of late church taxe)

Once you have registered, this will trigger the process to get your tax number (Steueridentifikationsnummer)

Last thing, is you will definitely need to register for a health insurance (Krankenkass), that part is Mandatory. (Unless you make a lot of money, you'll have to go with the normal system, Die Techniker is what I went with (good support in English))