Hi, I just come back from Istanbul, Turkey with my friends from a robocup competition which is held there. We've got a 10 days trips ( paid by school -- haha) and really enjoy there. Turkey is a modern Muslim country, they have many places to visit. You could come to the Museum, Church...they got quite a lot of ancient building to view. The price is around 10 euro per ticket. You can also take the sight seeing bus for around 20 euro. After visiting some famous places, you could take some tour for some beach in some islands ( around 60 - 120 euro) per trip. Or going to some high mountains there ( same price 60 - 120 euro).
For shopping, don't go to the market ( they charge u double price or even triple price when u speak English). You better buy something at the supermarket and shopping store on the street. We have walked around a few days, visit many stores before we bought some things at the final day where we could find a store with reasonable price ( To be honest, we just students --- haha).
If possible, you could spend some days at Istanbul then go to Sofia and Budapest, you really have a nice trip then. And the price is much cheaper than when you visit Paris ( I was there before --- school pay, offcourse)or London.