I love London, it's a fantastic city- yes it is pricy all around but definitely worth it. Anyhow, LHR is more convenient as it is closest to the city and you can take the tube. LGW has coach service and regional train service as well as the Gatwick Express (terribly overpriced), but the tube does not make it to LGW (at least not that I am aware of).
As a side note RDU-LHR on AA I have heard is kind of easy to make as a nonrev as the route exist mostly due to heavy subsidies from Smithkline Beecham, then again this is the summer so basically most flights to Europe from the US go full or close to full. I know our CLT-LGW flight at least in the summer usually goes full or close to it.

Regards,

Chepos