You can live in Stockton I here for 20 years and still be that odd ball that moved there from London
It is a good drive out and back and that is why Napton on the hill and Stockton are much cheaper - Southam just got a tesco so will be more attractive.
Warwick and Leamington have decent state schools, you can apply for stratford grammer and there are a lot of girls on the bus in the mornings from Leamington and Warwick.
Kenilworth has an older feel to it, there are a considerable amount of more mature people living there.
What do you want from a place - walking to shops and school or driving everywhere? What type of house, new, old, regency, cotage, modern village house. Be aware most of the villages are lovely- but deathly in the week as they are commuters and no-one is around.
Whereas W&L will be easier to make friends have coffee, join play groups, gyms, golf, swimming - two municipal pools, two main parks and several smaller parks. College for further education/night school stuff e.g silvermaking, cookery etc.
None of the secondary schools are bad anymore and choice is more relevant and where you live for access to schools is going to change anyway.
Junior schools the best two I know are Leek Wootton and Coten End