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I think you would need to start early in the day, target Hagia Sophia and then Topkapi Palace in the morning, having lunch in the Topkapi Palace with views over the Bosphorus...
In the afternoon, have a look at the Blue Mosque, Basilica Cistern then wander to the Grand Bazaar
Have dinner at somewhere in Sultanahmet
For the other day, wander down Istiklal Cadessi, keep eye out on the architecture of the buildings and side streets (some interesting shops in the sidestreets)..., grab a cab and cross over the Golden Horn to the Chora Church
Get back into the central area by cab and have a look in the Spice Bazaar and surrounding mosques
In the evening, cross over to the Asian side by ferry to view the sunset.
*check opening days and hours of attractions
Both suggestions are spot on
Food/wine are cheap as well as taxis