To add to what EatYourVeg wrote:
if you want walking distance of the station you really ought to be south of the river Medway.
I lived just off Dryhill Park Road for a few years, and that's a 20-minute walk to the station, which IMO was fine.
If you are not limited to being within walking distance of a station then I'd go for an outlying village. Bidborough Penshurst Weald and Leigh all have village primary schools, chipstead and otford are nice areas too though I don't know if they have primary schools. Underriver is very nice but no village school, your nearest would be weald or maybe seal which has 2 primary schools.
Otford has a primary, and also has St Michael's Prep School, which has a good reputation, although since my mum stopped teaching there it can't be as good as it was. ;)
MissWooWoo
we like TW but didn't want to go as far down as that due to the extra commute, we had a quick look around Tonbridge but the high street totally put us off!
The High Street is pretty awful. However, the Farmer's Market (2nd Sunday of every month) is brilliant (3,500 people through it every month), the Waitrose is just off the high street, there's a nice new middle-class cafe opened up. There are a dozen gastropubs within a short walk/drive/train journey, depending on where you are (Little Brown Jug in Chiddingstone is an 8-minute train journey from Tonbridge station, which means you can both drink if you want to).
And our history is WAY older than TW and 7oaks. There's some masonry in Tonbridge school which is apparently from a Roman temple which was once on the Medway (probably where the 11th C castle is).