As earlier post said Staines isn't bad and Ashford just east of Staines id even better as it is inside the turns for easterly deaprtures when on westerlies and westerly departues when on easterlies-if you follow
Kingston is also good but not Richmond or Twickenham
South London has most LHR inbounds too high to notice now Concorde is gone
Few places in the general more central City area itself are free from Heathrow noise except when LHR on easterlies. However unless you live on the extended centre lines for the westerly runways it isnt really a problem given the general level of noise in London. Easterly departures do not route over anywhere that can be called central. However the landing traffic can be noisy and I was astonished this summer when visiting a friend at how intrusive the approach noise was in Clapham a good 10 miles from LHR
Good luck