Last Chance Harvey

Divorced American Harvey Shine writes jingles for television commercials, a job not in keeping with his one-time aspiration to be a jazz composer and pianist. His position at work is tenuous as he departs for London to attend his daughter Susan's wedding. Upon arrival at Heathrow Airport, he encounters Kate Walker, a single Londoner who collects statistics from passengers as they pass through the terminals. Tired and anxious to get to his hotel, Harvey brusquely dismisses her when she approaches him to ask questions.
Harvey is upset to discover his ex-wife Jean rented a house to accommodate family and friends from the States but failed to include him. At the rehearsal dinner on the night preceding the wedding, it becomes increasingly clear Harvey is systematically being excluded from the clan around his ex-wife's new husband Brian and is treated as a mere guest. They fake their politeness towards him and make him feel embarrassed and uncomfortable. When Harvey tells Susan, with whom he has shared a strained relationship since his divorce, that he will be attending the ceremony but not the subsequent reception because he needs to return to the States for an important meeting, she informs him she has asked her stepfather Brian to give her away.
Meanwhile, Kate is on a blind date that is not going well. When she returns to the table after taking yet another call from her neurotic mother Maggie, who is certain her Polish neighbor is burying bodies in a shed in his yard, she discovers her date has invited friends to join them. Feeling unwanted and excluded from the conversation, she eventually excuses herself and goes home.
The following morning Harvey attends the wedding but quickly leaves for the airport without congratulating the married couple. But due to heavy traffic delays he misses his flight at Heathrow. When he calls his boss Marvin to advise him he will be returning a day later than planned, he is fired. Determined to drown his sorrows, Harvey goes to an airport bar and sees Kate. Recognizing her from the day before, he apologizes for his rude behavior. She initially resists the attention he is paying her but soon they're both glad to finally have an honest conversation about what they're feeling and thinking.
Harvey follows Kate to the Heathrow Express and, upon arrival at Paddington station, asks if he can walk her to her writing class on the South Bank. She accepts his offer and is pleased when he offers to meet her after class. As they stroll along the River Thames, Harvey mentions he is missing Susan's wedding reception, and Kate urges him to go. He finally relents, but only if she will accompany him. When Kate insists she is not properly dressed for such an occasion, Harvey buys her a dress and the two head to the Grosvenor House Hotel, where they are welcomed coolly by Susan and get two places at the children's table. When the father of the bride is called upon to make a toast, Brian rises and begins to speak until Harvey interrupts. He then delivers an eloquent speech that redeems him with his daughter and endears him to Kate.
Immediately following the first dance of the bride and groom, the groom calls Harvey up to dance with his daughter for the Father-Daughter Dance. He happily does so, and then all the guests join them on the floor for the rumba, tango and other dances, with Harvey enjoying himself on the dance floor, alone. Kate is left at the table, once again in the same position as when she was on her blind date. Her smile becomes more strained as she looks about and sees herself alone at the table in a room of strangers for several dances, Harvey having apparently forgotten she was there. When she surmises he will not be coming to ask her to dance, her smile disappears and she quietly leaves the room and stands in front of the elevator, preparing to leave.
Harvey, now looking for Kate, goes into the corridor and seeing her waiting for the elevator, he disappears into a side annex with a piano and begins to softly play one of his own jazz compositions for her. She hears the music and follows it, finding Harvey smiling and waiting for her. He asks her to return to the reception to dance and stay with him. She smiles and agrees.
Following the reception, Harvey and Kate walk and talk until dawn. They exchange a single, gentle kiss and agree to meet at noon. At his hotel, Harvey experiences serious heart palpitations and is rushed to the hospital, where he receives a call from Marvin who, having discovered his employee is more indispensable than he thought, urges him to return to work as soon as possible. Harvey decides he prefers to remain in London and explore the possibility of a relationship with Kate. He tracks her down at her writing class and reveals why he missed their rendezvous. Overcautious about romance because of so many past disappointments, Kate initially resists his suggestion that they see what the future might bring them, but finally agrees to give things a chance.
As they slowly stroll away, Harvey invites Kate to ask him the questions she would have asked him at the airport terminal, and this time, he happily answers, telling her his place of residence "...is in transition."

Question: Where is Harvey trying to catch a flight to?
Answer: Heathrow