easylife

I can't tell you where the 'terzi' are but a shop selling material will be able to direct you. The fabric shops are situated on the Cankaya side of the Kameralti (the main bazar area of Izmir.
If you are starting from the square in Konak where the little cami (mosque) and clock tower are, with your back to the sea, the entrance street is to your right, I think it's 866 sok/Anafartalar Cad. Just keep going up that street, after about 200m it bares right and when you get to the T junction at the top (it's quite a way), go left and the fabric shops are in streets on the right.
I'm afraid the Kameralti is a bit of a rabbit warren so good luck.