I would like to know if there is a way to use the findNearByPostalCodes API using placename for the city and a state to qualify the search, I tried putting the state abbreviation in the adminCode1 parameter but that does not seem to work.
This is not supported by a single call. You would need two calls, first to get lat/lng for the place name and then to get the nearby postal codes. The direct one call service is only supported for postal codes instead of place names.