I was in Istanbul in 1970 when I was 13, (my parents and I had travelled there with our caravan but that's another story!)
Off the top of my head I would say you need to visit:
Blue Mosque - you had to take your shoes off and leave them outside with a guard!
Saint Sofia church (opposite blue mosque, and much older than our cathedrals)
Topkapi museum (I think this is in the same area too, loads of beautiful jewels etc.)
Bazaar
I don't have any up-to-date info on prices, routes etc. I'm afraid
When we were there we bought fresh lemonade from stalls (despite warnings it might be dodgy, we were so hot!) and freshly caught grilled fish in bread straight off the fishing boats near the Galata bridge near the mosques...wonder if they still do that...they actually had BBQs cooking IN the fishing boats!
We went on a boat trip, supposed to be round the Bosphorus (? if I remember right?), had those little glasses of black tea on the way, but it deposited us at a a place we discovered was on the Asian side of Turkey
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and wasn't returning for several hours so we had get ourselves back into Europe and found a train back into Istanbul, over the bridge. That was an adventure!
ooh it's bringing back memories ( hope i haven't gone off-topic?)
I've just found this, if it's helpful?
http://www.lonelyplanet.com/worldguide/destinations/europe/turkey/istanbul/
Hope you have a wonderful time!