I've been to Istanbul
several times. Here are some ideas.
It's pretty easy to spend several days seeing the sights in Sultanahmet, the old city & major tourist destination
, especially if you are into historical sites. Blue Mosque, Aya Sofia, Topkapi etc. If you like museums, the archaeological museum near Topkapi is excellent and extensive, I spent most of a day there.
If you want to see more of modern Istanbul I'd say go to Taksim square and walk down Istiklal Caddesi -- a long pedestrian mall. Go during the evening rush and it is a sea of humanity, great people watching.
My favorite things to do in Istanbul though, reflect my tastes & maybe other cruisers will appreciate these too:
First, the Bosphorus Tour on the Istanbul ferry
which goes from the Eminonu ferry
terminal all the way to the mouth of the Black Sea at Anadolu Kavagi. There you can walk up the hill to the Yoros Castle with a nice view of the mouth of the Bosphorus. Keep an eye on the schedules so you don't miss the ferry back. There are also small private boat tours which only go under the two bridges and back, not nearly as good as the full trip on the big metro ferries.
Second, take the ferry to the Princes Islands - I went to Heybeliada. There you can rent bikes and bike around the island. In the summer there's a nice beach where you can take a dip, not so practical in the winter.