Off duty, police officers cannot enter places like post offices, hospitals, mental health providers, banks, airports, bus stations, train stations, and other places with strict gun bans as far as I know. While off-duty, all but elected and federal officers like US Marshals and FBI agents are considered off-duty and civilian when not working. Exceptions in airports are made for officers who have met certain criteria and are transporting criminals from one jurisdiction to another, but they have to meet a long list of criteria, including special permission from the TSA itself.