I lived in Greenwich for 8 years while we were in London and loved the area. My husband also worked in Canary Wharf so its a quick commute. Canary wharf also has a great shopping centre so you don't really need to go into Central London as everything is there. There are cinemas, lots of bars and restuarants and gyms. The park at Greenwich is fantastic and they have a great farmers market every weekend. There are some great walks along the river and even a city farm at Mudchute. In winter there is usually an ice rink in the maritime museum. Blackheath is close by which is a lovely little village with parks, shops and restaurants. At North Greenwich there is a huge Sainsbury's, cinemas and B&Q. You can easily take a bus into central london, or the underground, and they have the Docklands Light Rail to Canary Wharf or its an easy bike ride.
Wimbledon and Hampstead will mean a long commute to Canary Wharf, at least an hour and I wouldn't want to rely on the London Underground for that every day.
Sorry I can't comment on schools, but check out the link that Karen bt posted