Even if you're not a huge fan of modern art, a visit to the city's leading contemporary art exhibition space is worth it for the beautiful views across the confluence of the Golden Horn and Bosphorus to Saray Burnu (Palace Point), the tip of the historic peninsula crowned by the Topkapi Palace. Then there's the fancy Istanbul Modern Restaurant (open daily 10am-midnight), a cut above the average in-house gallery eatery—especially if you can commandeer a table on the terrace right above the water—and an in-house cinema with regular screenings (TL9). If that's not enough, you can while away a few hours admiring a brilliant selection of art books in the library or browsing through art prints and the like in the trendy shop.
But what about the art? Few foreign visitors will be able to name a single Turkish artist before coming here, so start with the permanent collection on the first floor, which whips through the origins and development of Turkish art from the late-Ottoman period through to the present day. There's some great stuff here, with Turkish twists on most of the important movements in modern world art. Past temporary exhibitions have varied wildly in theme and scope, from modern Turkish architecture to Japanese comic book art, Magnum photography to retrospectives of major Turkish artists.