I am from Greece so I didn't visit the highlights (Acropolis, Plaka, Monastiraki, Theseion). My advice: don't follow an excursion, unless there are health reasons for that. Just take a cab, go to Metro Station at Piraeus and then just follow the line. Get off at Theseion and walk to Acropolis and the Acropolis Museum on foot taking one of the most wonderful pedestrian streets in the world, called Dionysiou Areopagitou.
I couldn't say too much because Istanbul is immense and has so many beuatiful places that you can get lost! All I can say is that the 1-2 days cruises offer are not enough. However, if you have to choose: cross the Galata bridge, find the Egyptian Spice Market and let your nose rejoice! Then, after a short walking distance to the left of the market, visit Agia Sofia, the Blue Mosque and Cisterna. If you have stamina, take a cab or a bus and go to Capali Charsi, the Grand Bazaar an then go bask to the ship to refresh. In the afternoon you can explore the "european side": You can Walk to Galata Tower and take a cab or walk to Istiklal a boulevard with shops of all kind that will lead to you to Taksim. In the little passages at the sides of Istiklal you can find many cafes and restaurants that are lively every time of day and night. If you have a second day in Istanbul, take a bus or cab and visit Chora Monastery and admire the unique byzantine mosaics. You can walk from there to Fanari, a once greek area, really picturesque, and then take a bus to Dolma-Bakche Palace and Okoy. There is a Mosque there and a very picturesque spot.
Insanbul (Constantinople) is a fairytale!..
It is the celebrities and "the wanna have fun and try everything" for youngsters during the summer. At the time we visited, it was windy, but still crowded. For me, it is not worth staying at the capital. It is not authentic anymore. Ask about other villages and get a cab or a bus to go there. If you are interested in archaelogy, take a ferry to Delos.