If you’re only mentioning a single airport, use its full title, including the IATA code.
However, it’s better to be concise when listing multiple airports that have commonly abridged names, like LAX and JFK. Where no commonly abridged name exists, use the airport’s full name.
“The Embassy Suites Shady Grove is close to all local attractions and within easy reach of Memphis International Airport (MEM).”
“The Hilton London Metropole offers excellent transport links to surrounding airports, including Gatwick (LGW), Heathrow (LHR) and Stansted (STN).”