Antony,
Consider Canada, our rates would be very competitive relative to the US$, and if I'm not mistaken the ICAO license you could earn in Canada may be closer to an EASA license than an FAA license.
That said, consider removing the word "cheap" from your thoughts. it is up to you to determine the cost effectiveness of the services you choose. You are proposing to join a skilled group, and we would rather not be branded "cheap" no matter what aviation service we provide. Of course, you will find a range of pricing for a similar service, but peripheral characteristics may be difference, and it's up to you to evaluate.
But at the end of the day, would you like to proudly announce to your passenger to be, rental aircraft provider, or insurer, that you learned to fly as "cheap" as you could? 'Sure puts you in a poor light as a pilot! I would be much more proud to state that I "carefully selected a flying school which fit my needs".