I was in Istanbul for a week about 2 years ago. Great place.
I stayed in Sultanahmet area which is nice but it might be better to stay around Sirkeci Gari station. There are some nice, cheap hotels round there ($50/£35 per room). It's a good idea to be near the water as you will be crossing the river by ferry very often to get to other parts of the city. The Galata area would also be OK
Can't remember all the names of everything but any guide book will show you all the important mosques and there's two palaces worth seeing. It's also nice to hang out in the local bars and cafes watching the world go by.
There are no secret undiscovered castles or islands, what you read in a guide book is what you get. I recommend a trip on the ferry to the far end of the Bosphorus. You'll love it and it takes up many hours. Bookable at any ferry port.
There is a cheap mini bus from the airport but I couldn't find the ticket desk and so had to take a taxi instead. Getting the cheap bus back to the airport was easy and bookable in most hotels or travel agents. Maybe the bus is better displayed at the airport now.
Outside the city:
There are some islands they say are nice but the ferry was irregular and I was told not worth going out to in winter. There is enough to see and do in the city so no need to think of exploring further.
For some reason, from my observations, females do not like Istanbul. I think they get oggled at. It's men everywhere. If she dresses conservatively and knows that the guys will be checking her out, she might find it amusing.
My pet hate was the Indoor bazarre. You get hassled and you can't stop to look at anything. I liked the different outdoor markets mainly for the atmosphere. The food everywhere is brilliant.
Hope this helps. Need any more info, let me know.
and with that..cabin crew, seats for landing please.