Good advice from mmack there. A trip on an ordinary commuter ferry is a great way of seeing Istanbul and the Bosphorus. Who cares if you do it on this visit and do it again with your wife! The busiest ferry terminal is probably Eminönü; explore some of the routes and go on a trip up the Bosphorus. There are some delightful restaurants along the waterfront on the European side of the Bosphorus, at places like Ortaköy, Sarıyer and Bebek; stop off an explore some of these suburbs.
The Rüstem Pasha mosque, which is up the hill from the wharf at Eminönü, has some of the most exquisite İznik tilework you'll ever see. It is a little hard to find, but believe me it's worth it. So you could spend an interesting half-hour or so finding it on this visit and then be able to take Mrs Marzomarz straight there when she comes along next time. As I say, it warrants a second visit.
St Saviour in Chora, just outside the old walls of Constantinople, is worth visiting for a different type of artwork and is a stunning example of a Byzantine church, still extant.
If you're ever planning a trip in the tulip season, try the Emirgan Park at Sarıyer for the most fantastic display of the flowers. The Tulip Festival is held in April every year. And the views over the Bosphorus are pretty good too. Nearby is the Sakıp Sabancı Museum, which hosts some interesting touring art exhibitions.
Just a few ideas...