Ok intriguing puzzle! So your classic north London up-market suburbs would be Hampstead, Highgate, Muswell Hill or Crouch End. All very 'villagey' and classy with leafy streets of Victorian villas, good parks, easy access to all the North London preps and great shops, restaurants etc. You'd have an easy commute from any of them, Hampstead and Highgate have the Northern line which will get you to Kings Cross or Tottenham Court Road etc in under 30 mins, Muswell Hill has Ally Pally station which again is on a line into Kings Cross and from Crouch End you can catch a 5 min bus to Finsbury Park which is very quick into Kings Cross or Warren Street.
You might end up feeling a little short changed on the house and/or the garden at that price though. A few ideas of what your money would buy...
www.rightmove.co.uk/property-for-sale/property-75209714.html
www.rightmove.co.uk/property-for-sale/property-67841062.html
www.rightmove.co.uk/property-for-sale/property-75870326.html
www.rightmove.co.uk/property-for-sale/property-66257185.html
www.rightmove.co.uk/property-for-sale/property-75781076.html
Alternatively if you are willing to look a bit further out, consider Totteridge or Mill Hill village (which both feel very rural despite being surrounded by much less nice areas) or Radlett or Hadley Wood which are really small towns right on the edge of London and with a train line direct into Kings Cross (beware the trains are super busy in the morning but I think it's something like 30 mins on the train into central London from each). Again some idea of the quality of housing...
www.rightmove.co.uk/property-for-sale/property-67539494.html
www.rightmove.co.uk/property-for-sale/property-53032284.html
www.rightmove.co.uk/property-for-sale/property-67302826.html
www.rightmove.co.uk/property-for-sale/property-74398178.html
www.rightmove.co.uk/property-for-sale/property-76168850.html
www.rightmove.co.uk/property-for-sale/property-64763170.html
And then again if you are prepared to not be in London at all you could look as far afield as St Albans, Welwyn Garden City, Hitchin etc where again you would be at Kings Cross in well under an hour and your money will go further again... all of the above have good school options although perhaps less choice and less high-flying/fancy than the North London preps, which may be a good or a bad thing depending on your POV!
I think personally if given the option I'd choose to live in Highgate or Muswell Hill and have a shorter/easier commute. Plus if you are thinking of Highgate, Devonshire House, South Hampstead, NLCS etc that would mean a shorter commute to school - getting into the suburbs from the outer regions can actually be much tougher with traffic etc than commuting into the centre on the train. Whereas if you are going for one of the smaller preps or one of the 7-18 schools like Mill Hill, Radlett or Habs you might be better off going for the bigger house and slightly further out!