Dear @Jeddy,
Welcome back to the Wefugees Community and thank you for reaching out to us again. I am afraid that "escaping" the assigned city without a regular procedure may lead to problems. Section 60 of the German Asylum Law (Asylgesetz) explains the so-called "Wohnsitzauflage" during the asylum procedure. The biggest chance to get a permission to move to another place may be to find a job in the respective city. However, you will need to apply for the transfer/moving at the immigration office (Ausländerbehörde) and wait for a positive answer.
Do you agree dear @mbeon-ruth and/or is there anything you would like to add?
Best,
Meike