The most pleasant way to see the sights along the Golden Horn (map) is on a short ferry cruise.
Sleek modern Şehir Hatları passenger ferries depart Üsküdar hourly on the half-hour (or shortly thereafter) from 07:30 am to 19:45 (7:45 pm), cross the Bosphorus, glide beneath Galata Bridge to dock at Karaköy, then Eminönü (map) at 45 minutes past the hour, then cruise up the Golden Horn (Haliç) stopping at Kasımpaşa, Hasköy, Ayvansaray and Sütlüce before terminating at Eyüp.
Here's the full schedule on the Şehir Hatları website.
A Golden Horn cruise is great for photographing the city, takes just over a half-hour from Eminönü, and the fare is only TL3 single/one-way!
Along the way you pass the cast-iron Church of St Stephen of the Bulgars, the Fener neighborhood with its Ecumenical Orthodox Patriarchate, the formerly Jewish neighborhood of Balat, the Ottoman Tersane(shipyard), the Feshane, a former fez factory converted to an art and exhibition hall, and finally, Eyüp, the favorite burial-place of Ottoman nobility, well worth a visit. More...
The return voyage departs Eyüp at 08:30 am, then hourly on the half-hour or shortly thereafter, then on the half hour until 19:45 (7:45 pm).
A final voyage departs both Üsküdar and Eyüp at 20:45 (8:45 pm) daily except Sunday and holidays.
To board the ferry at Eminönü, from the southern (Eminönü) end of Galata Bridge, walk west along the Golden Horn shore past all the TurYol boats, toward the prominent T. C. Istanbul Ticaret Üniversitesi building, to the small, somewhat hidden Eminönü Haliç İskelesi(Eminönü Golden Horn Dock), a small wooden building. This is where you board the ferry.
View Golden Horn (Haliç), Istanbul, Turkey in a larger map