When I lived in the UK, I lived in Beckenham ( bromely)... You can take the tram( which starts at around 4:00 am) to east croydon station in about 15 minutes.. then its only a short and chep train trip to Gatwick.. and I've taken trains at 3:00 am going there and back.. also the N2( which goes as far as Crystal Palace.. then a short cheap cab ride) or the N3 are very convenient for getting home from London in the wee hours..also trains from clockhouse ( to Charing X) and beckenhman junction into victoria only take 25/30 minutes.. zone 4.
When I go back and visit family, I have no trouble getting to gatwick.. I THINK there is also a bus from Bromley that goes at all hours to Gatwick..
beckenham is fairly nice and family-ish, its easy to get to London too.. and as I said, easy to get to Gatwick