Stoke Newington is very nice - it strikes a great balance between being very slightly Bodeny and near nice parks, but still being Hackney, so it's quite trendy and 'real' (by real, I mean you'll get the most amazing food really cheap, including at a Turkish place where Gilbert & George eat every night, and great music venues, etc.). If you're looking at Hackney you should also consider the Victoria Park area - it's very sought after, very beautiful (the Park is immense and a huge local community meeting-point, and beloved by everyone), and rarely for Hackney is near a tube (Bethnal Green).
Also - one other thing - now that I've lived here for so long (coming up for 10 years) I can't imagine what life must be like to have to travel and make real efforts to get to world class art/museums/music/events etc. Of course, there is plenty going on all over the UK, and I wouldn't say for a minute that all culture outside London is worthless, but there's something incredibly special about being a bus ride away from, say, the British Museum, or the Barbican, or Borough Market.
I've also noticed the difference between kids brought up in London and those brought up in small towns - I have lots of nieces and nephews that come and visit, and they tend to be a bit alarmed by the Tube, the hustle and bustle etc., whereas kids brought up here wouldn't be fazed by anything (except possibly a herd of cows).
Greenwich? I thought you wanted to live in London? 
Just wondering though - how much could you bear down-sizing on your home or would it not be that much of a problem for you?