Pros +Blackheath is much more relaxed than other areas of London. Ive lived in Hackney, Clapham, Elephant & Castle and all were much more hectic than this area.
+Theres some lovely bars, restaurants, cafes shops etc in Blackheath and Greenwich, not to mention Greenwich market with the fabulous Portuguese food stall.
+Theres many lovely period houses and there are areas which are much more reasonable than comparable places in London.
+The whole area is very green with loads of trees & open spaces. Greenwich park is on the doorstep and is fantastic at all times of the year for Adult walks, kid walks, great playground.
- Its only 25mins drive to bluewater. Its also easy to drive north of the river. I regularly drive into the city in 30mins (off peak) and woodford 25mins.
Cons- public transport in the area is not as good as other areas of London. Having said that Blackheath has good train service to Victoria and London Bridge, you can use your payg oyster card now too.
Do spend some time here before you move so you make sure you pick the right area for you. 'Blackheath' can span a wide area in estate agent talk and all areas are different- eg the Village is v different to the Standard. Both are great- just for different things. Personally I like the Standard. It's much less pretentious and the m&s, bakery & library give it the edge! Hope this helps. Shout if you want more specific help.
PS Watch out for the Blackwall tunnel closures over the next few months.