I find this a slightly strange question because St John’s Wood is so very close to the centre of London. It doesn’t have its own train station, but it’s on the tube and well-served by tube & buses from central London.
You could pick one of the outlying tube places, like Amersham or Chesham, then take the Metropolitan line into London, change to Jubilee Line for St John’s Wood, but it’s a slow busy journey.
Otherwise any “burg” outside of London will have you travelling into central London first (and bear in mind it’ll almost certainly be a busy commuter route) - Gerrards Cross for example would involve a train into Marylebone (central London) then a long walk/short bus ride back out to St John’s Wood. So I would generally suggest just staying in London itself ... you could look at Marylebone area or Little Venice or St John’s Wood itself, which have a slightly villagey feel.
Otherwise have a look at train services that go into Paddington or Marylebone, the two mainline London stations nearest to St John’s Wood. But bear in mind that would mean travelling into central London first then up to St John’s Wood by bus, tube or foot.
But London is so big and St John’s Wood so close to the centre that you’d be looking at a long journey full of commuters whereas to get to St John’s Wood from central London - say Baker Street area - is a matter of minutes.
