You can currently use the Hungary and County passes on local buses in these cities:

Local transport: County passes can only be used on local transport (metros/trams/buses) in the following cities: Budapest, Csongrád, Esztergom, Érd. Zalaegerszeg until 31st December, 2024.

Daily tickets do not allow you to use local transport except Érd (although you can use interurban services between stations within any city).