Hi,
Well there is only one English-speaking school and that is TISA, The International School of Azerbaijan. My daughter attended this school for two years back in 2010 -2012 and she loved it. We left then to come back to the UK but I can tell you it is absolutely excellent. I was fortunate in that BP paid for the school fees so I am not sure if you would have to pay out of your own pocket. But an excellent school.
Hope this helps!