Is there a home allowance for Arbeitslosengeld II recipients?

No, you do not have to go to a residential area, because the rent including heating costs is taken into account by the institutions of the Grundschutz für Arbeitsebende when calculating your benefits. However, only up to a certain upper limit, the expenses for rent and heating must be in a “reasonable” framework.

vgl. Wohngeldgesetz und § 5 SGB II