In Istanbul you should go to the citypart of Sulthanamet. In this part you can find the blue and Ayasofia mosque. There is good budget accomodation and good restaurants. From there you can explore the rest of the city and going to the Asian part of Istanbul (at the other side of the Bosporus).
Turkish people are good and friendly and most people speak a word of English. You pay with Turkish lira. When I was there US$1,- was 1.600.000 lira. They have skipped all the zeros some weeks ago (not sure!!), so one dollar is now 1,6 Turkish lira. Public transport is good and cheap, the taxis use their meters. Its not much hassle to travel trough Turkey