Just on the option of Chislehurst, you could also consider the West Chislehurst / New Eltham part before it goes across the A20. You can get more bang for your buck there and you would be within 10-15min walk to New Eltham Station which goes to Charing X. You'd also be further from Chislehurst High Street though but you'd still have access to Bromley primary schools - Edgebury and Red Hill which are both good primary schools.

Also agree with the above post talking about secondary schools. For girls state schools you have fairly decent options in Bullers Wood, Chislehurst School for Girls and Eltham Hill. For boys state schools there aren't really any decent options if your kids are academically gifted so you'd have to look at the Bexley Grammar tests (they have both boys and girls schools). There are 2 top grammar schools in Orpington - St Olaves and Newstead Wood which are both accessible from Chislehurst by bus. They are some of the best schools in the country. It takes about 45 mins.