I'm not sure Eltham is 'gentrifying' material, but there are beautiful, big open spaces, great Victorian/Edwardian housing, and just a quiet, peaceful feel. Mottingham, up the lane, has some attractive houses, history - around Eltham College; riding stables, and, of course, Eltham Palace. For Catholics, St Thomas More , in Eltham, is a good secondary school.
The association with the horrendous circumstances of the murder of Stephen Lawrence may put some off, but I believe things have long been changing for the greater and diversity is taking its natural hold.
The ex-local authority houses between Eltham and Kidbrooke are exceptionally pretty - placed on their greens - reasonably priced and, I'd have thought, very appealing to young families. Sure the rail link to London isn't the best, but the trains go through Lewisham to London with the option of Lewisham DLR, and not that infrequent.