Hope you find someone in Cairo, but in the meantime have you looked at the Turkish language primer on the TurkishLiving forum? It's very good and you can pick up a lot.
Have you checked craigslist? Post an ad and see what you get back ...you just never know and it is free. Turkish must be difficult or I think it would be to American ears.
I think it would be really neat if they had an intensive language school that could provide you with Turkish classes for a few days, just to get your feet wet!
For me it would take more than a few days! I once got very interested in learning Catalan because I think it's so pretty as a language and I was spending time there. I know some Spanish but it turned out to be quite hard!