For Bromley, you do need to be careful exactly where you live and probably have secondaries very much in mind when you do. Where we are, Bullers Wood secondary is well regarded for girls and there is a boys' version supposed to be opening in the next couple of years I think (not relevant to you at the moment, but you never know). Although Bromley is not an 11 plus area, a lot of people do the Kent and Bexley tests, but you could have a fair commute on your hands with that. Newstead Woods (for girls) and St Olave's (for boys) are the Bromley borough super selectives, NW being based in Orpington.
In Bromley itself (I don't know the rest of the borough) primary schools are all pretty good from what I hear but you need to virtually live in the playground of some of them, like Valley, Bickley Primary School, Raglan and Parish. If you are RC there is St Josephs (to consider, which is a one form entry but good. There are also a number of new primaries, including a Harris Bromley.
Last year a bilingual French-English free school opened - La Fontaine Academy. It has had some very good reports but is currently in temporary accommodation and, so far as I know, has no permanent home identified yet.
As to the area, it is good with decent transport links into London and out to Kent and the coast. It has no tube or DLR as yet, though that may change in the future. As already said, for £850,000 you should get a very nice house but do be careful where you choose. For example, the Palace Estate is lovely, but parts of it have been a black hole for primary schools because they are beyond the distances of many of the nearby ones (I am not sure if that has changed with the opening of the Harris school and the recent improvement of St George's Bickley, but it is still worth researching).
If you end up choosing private school for any reason, there are quite a few good options in Bromley.