London for 3 months

We are a family of 5, from the US, with 3 children between the ages of 8-12.  My husband will be working in London for 3 months this fall and we will all be "moving over" to live with him.  We will need to be within an hour or so of both Luton and Farnborough.  Any recommendations on areas that would be best for our family to reside during this time?  We would be OK in the city, but prefer some outdoor space.  Ideally would like somewhere we can use public transportation only, parks/playgrounds, good restaurants/markets, and other children to connect with.  Thanks for any direction you can give us.

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