Question Best London Neighborhood for a Quick Stay Before Heathrow Flight

We have to take a 9:00 international flight from Heathrow on a Tuesday morning. That gives us just one day and night in London. Can anyone recommend a neighborhood to stay in that's convenient for getting to Heathrow early in the morning but also offers a good experience of London in a short time? We're interested in easy access to some iconic sights or a vibrant area to explore, even if just for a few hours. Any suggestions on where to stay would be greatly appreciated!