Where to live in or around London?

Thank you all so very much.  I'm used to NYC where, at least in Manhattan where I lived, it was very densely populated and you were lucky to even have the smallest balcony for your outside space.  It's nice to hear that there are areas of London that have an more of an open feel to them.  I guess when I have visited in the past or were there for work I stuck to the central part of London.

Clapham looks like a possibility ("nappy valley" - he he) and I'm still investigating the suburban options too.  I really, really appreciate all your advice. 

Richmond is lovely and might have that Greenwichy feel that you're looking for.  There is a nice town center with all the shops and restaurants and other amenities that you need.  There is a Whole Foods opening in 2013 or 2014 right there in the center.  There is plenty of green space as well as the river and you should be able to get 3 bedrooms with your budget.

Visited London many times and looked at many areas due to potential relocation. The only area that I absolutely adored was Richmond. Very picturesque.