Situated on what were once the grounds of the Topkapi Palace, this fantastic complex, right in the heart of the Old City, is quite literally crammed with some of the finest antiquities you'll find anywhere in the world. And it's all the better for being sadly neglected by the hordes of visitors rushing between the sights widely-perceived as Istanbul's major players—the Blue Mosque, Grand Bazaar, Hagia Sophia, and palace. Their loss is your gain, as you can admire everything, from the oldest peace treaty known to humankind to exquisite 3,500-year-old jewelry unearthed from the legendary city of Troy, in relative peace.
As you push through the electronic turnstiles into the three-building complex you're greeted by a couple of grinning black basalt lions, sculpted in the 9th century BC, flanking steps leading up to the first, and smallest of these buildings, the Museum of the Ancient Orient. Inside what was originally a fine arts college is a small but stunning collection of artifacts from ancient Egypt, Mesopotamia, and Anatolia. The highligh of the exhibits is arguably one of its least spectacular at first sight, a clay tablet inscribed with cuneiform script. This, the Treaty of Kadesh, is the first peace treaty ever recorded, signed between an Egyptian pharaoh and Hittite king in 1274 BC. Its significance has not been lost on the United Nations, and a replica has pride of place in the UN headquarters in New York. More visually appealing are the colorful tiles depicting various animals that once lined the approach to the Ishtar gate in Babylon.
The imposing main building of the Archeology Museum is diagonally opposite the Museum of the Ancient Orient. Don't be surprised by how European it looks, with its distinctive neoclassical façade, as its architect was the Frenchman Vallaury, also responsible for the famous Pera Palace Hotel and Ottoman Bank across the Golden Horn in Galata/Beyoğlu. A conscious and successful attempt by the late-Ottoman Turks to mimic the museums which had sprung up in previous decades in European and US cities, there's a bewildering amount to be seen here—so don't even try. Pick out a few sections that seem the most interesting and concentrate on them. There's always another day and the admission price is very reasonable.
Centerpiece of the exhibits in this building, on the ground floor, are the (mainly 4th century BC) sarcophagi from Sidon (in today's Lebanon) excavated by the museum's mastermind, artist/archeologist Osman Hamdi Bey. It's hard to believe that a mere mortal could have carved the relief battle scenes adorning the exterior of the Alexander Sarcophagus, so life-like are they, nor the ethereal mythical beasts decorating the Lycian Sarcophagus. Downstairs in the basement is a well-lit collection of Byzantine objects, while upstairs are finds from the ancient city of Troy. Not to be missed on the mezzanine floor is the Istanbul Through the Ages section. Spend an hour strolling around here and you can dispense with your "History of Istanbul" and see this great city's history unfurl—from its Stone Age beginnings to its capture by the Ottoman Turks in 1453—in a series of informative display boards and genuine artifacts (including links of the chain the Byzantines stretched across the mouth of the Golden Horn to repel enemy ships).
Opposite the main entrance of the museum is the third building in the complex, the Museum of Turkish Ceramics. In its past incarnation as the Çinili Kösk (Tiled Pavilion), it was a kind of royal box from where Ottoman sultans could indulge their passion for grease wrestling—a manly sport which has a foothold in the Turkish psyche to this day. It now houses an attractive collection of Ottoman tiles and other pottery. Next to it is a statuary littered garden area complete with half-decent café .