We had five days in Istanbul, still was not enough. Definitely do no miss the Topkapi Palace which is fabulous, even though we visited I would go back to see it again, an amazing place and you can get lunch or a snack there at a restaurant overlooking the river. There is also a gift shop in the ground which was the cheapest shop we found, run by the government, full of geniune Turkish items, all with prices on them.
Avoid the Grand Bazaar, hated it, huge place like a maze where everyone was in your face trying to sell, gave us a headache. Blue Mosque was also beautiful, don't try and see too much, plan to go back as Istanbul cannot be rushed.
One place we ate at was an Hotel "The Orient Express" which had a roof top restaurant where there were wonderful views of the city looking down to the water, the bridges and all the cruise boats. We were lucky enough to see a firework display from this vantage point. The place is open to the public. Food and service was very good, book and ask for a table near the front.
As Tribalelder says, buy a guide book, our hotel gave us a map and a guide book free. It's very easy to find your way around.