Which is the nearest Airport, if I have to travel to Harrow*?
* Harrow is a suburban town in the London Borough of Harrow, in the north-west of Greater London, England, 10.5 miles northwest of Charing Cross.
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There are 5 main airports in London. Gatwick is SWish, London City is in the inner east, Luton is north, Stansted is north east and far. Heathrow is in the west, and about an hour away from Harrow by public transport.
For fun, I plugged them all into Google to check times by transport (public).
From personal experience, avoid Stansted and Luton, and not many fly into LCY. So I'd be looking at Gatwick or Heathrow, mainly.
Geographically of the major London airports Heathrow seems to be closest. If you plan to take a cab or rent a car then Heathrow is probably the best, followed by Stansted and Luton. If you want to travel by car I would avoid Gatwick (other side of London) and London City (as the name suggests in the city centre) airports.
On the other hand if you plan to travel by public transport then distance often bears little relationship to travel time. Busses are slow and trains tend to go to/from central London. Neither of the Harrow rail stations is on the same rail line as any of the airports. Heathrow still seems to be the best, but after that as Mark points out it's a wash in terms of travel time (though probably not travel cost) between City, Gatwick, Stansted and Luton.
As Mark Mayo's answer shows, except for Stansted, the travel times from the major London airports to Harrow are basically the same. The differences between them aren't significant compared to other aspects of your journey. For example, flying at a time that's more convenient for you, picking a cheaper flight or a route with better connections would probably all make a bigger difference than the possibility of saving 15 minutes travelling from the airport to Harrow.
Mark Mayo provide a good factual answer about London's airports and David Richerby added a couple of good subjective points (cheaper flights, time convenience, etc.)
I would add that, from personal experience, if you are planning to travel by car, then Luton or Heathrow would be best, as they are roughly the same distance from Harrow and you'd be travelling through roughly the same volumes of traffic (possibly, a bit less traffic from Luton).
If you are planning on using public transport, then I would recommend Heathrow, as it's much better connected, with a variety of public transport options and you can get from Heathrow to Harrow on the Hill using only tube and public bus. Have a look at google map options and do note that on the Piccadilly line you can switch at Acton Town station, no need to go to Hammersmith - this would save you another 10 minutes or so.