On a world scale, an hour wouldn't get you that far, it would be eaten up by travel to / from airport. For example Charing Cross (often used as a location for the centre of London) is about 30 minutes by train / 40 by car from Heathrow Airport according to Google.
Google routed me to Paddington (via Bakerloo) and then the Heathrow Express. I was probably lucky with departure times when I searched though.
(Heathrow Express is expensive compared to the Underground though, but if you were making this sort of map you'd probably use it as it's the faster service).
