Unlike the previous two posters who spoke about Furzedown and Brixton, neither of which is Streatham, I am going to give you my impressions of what is actually Streatham.
Streatham is a big area - very very big for an area with a single name on it. The natural divide is between what's east of the main road and what's west of the main road. Each side of the main road can then be divided up further between what's north of Streatham Hill station, what's between Streatham Hill station and Streatham station and what's south of Streatham station. That gives you six different areas.
The nicest one of those six areas is that which lies west of the main road between Streatham Hill station and Streatham station, i.e. between the main road and Tooting Bec Common. There are some really lovely roads here - lots of mature trees and beautiful houses of a number of different types. I live in a terraced house in Tooting (accessibility of Northern Line and being able to buy a house we liked near a good state Catholic primary school) but if we were choosing just on the basis of house, house price and street we'd have chosen that part of Streatham. The shops/restaurants on the main street in Streatham are generally good and, a change from some other areas of SW London, very reasonably priced. Lots of independent shops, including fruit and veg shops and an Italian bakery which we stopped off at on Sunday and which was 1/3 the price of the equivalent on Northcote Road.
The Streatham Hub development is underway and is going to result in a Tesco supermarket (giving a bit of competition for the existing Morrisons but hopefully not killing off the independent shops), cinema and ice rink:
http://www.building.co.uk/streatham-hub ... 19.article
I don't know much about children's activities or schools in Streatham, apart from the Catholic school, St Andrew's, which is two form (60 pupil entry). St Andrew's is an excellent school. It only has a "good" Ofsted but if you read the actual report you will see that several aspects are outstanding and there is hardly anything to criticise. If you look at the KS2 results you will see that they are excellent. However, most of the other schools are middling, except for Telferscot, which is west of Streatham Hill - almost in Clapham Park - and Immanuel and St Andrew (Church of England) which is at the opposite end in Streatham Vale.
The biggest problem with Streatham is transport/traffic. The main road is effectively a through route between the M25 and central London. There is no underground. The main road has lots of bus routes, including ones going as far as Paddington and Liverpool Street, which is great late at night but not so good during the day when traffic is a nightmare. If you live some way from the main road you're unlikely to have a bus stop/route near your house and may have to walk for up to 15 minutes to get to one.
Streatham station has Thameslink trains to the City and also trains to London Bridge. Streatham Hill station has trains to Victoria and to London Bridge. I don't have any idea how busy these are at peak times. I guess it depends on where work is now / is likely to be.
As regards activities for children, I don't think it's anything like Between the Commons or Balham. However, I haven't checked it out for those sort of things. I would say that there are fewer businesses looking to guilt trip parents into wasting money. However, if you check out the internet you will see what activities there are.
Hope this is useful.