The Archaeological Site: When you first arrive you will probably head right up to the Lion Gate. Here is a piece of advice: Taking pictures of the 13th century B.C. Lion Gate (shown here in the picture) is not really easy. You will want to make sure the shadows do not ruin your photo because every picture I have ever seen taken by tourists (and even some professional ones) wind up with the gate being too dark to see the lions. You can see another example of this photo hazard at the Dilos Travel site's page on Mycenae. Just try to keep out as much of the bright sky behind the gate as you can. This site is so important that I heartily recommend a guidebook of some sort. The first thing you will stop at once you enter the gates is Grave Circle A, where Heinrich Schliemann in 1874 found the burials of 19 bodies and 31 lb.. of gold items. Upon seeing a gold death mask, Schliemann wired the famous line that ran in papers across the world, "I have gazed upon the face of Agamemnon!" The items are now kept at the National Museum of Archaeology in Athens, but a museum is being constructed at the site (it has taken them more than a decade to build it). You can learn more about the contents of the shaft graves here. Within the walls of the acropolis, you should visit the remains of the palace. The throne room and hearth are still clearly visible. You can also go down the 99 steps inside a cistern at the other end of the citadel. I only made it halfway, but found myself standing on a ledge where the steps turned, holding a flashlight in each hand trying to light the steps up one way and down the other for the other people in my group. When you get through with the acropolis and grave circle inside the walls, be sure to go down and see the tholos tombs below the acropolis (which can take alot of your time in itself). But you cannot miss the big tholos tomb across the street. It is also known as the Treasury of Atreus and you can go inside this one (the only one at the site which you can). I would like to thank Kim Shelton for her tour of the lower part of the site, especially under such laborious circumstances (sorry about the pun)!
Among the best web sites are the Ministry of Cultures' web page on the Archaeological Site of Mycenae and a picture tour of Mycenae at Tulane. You can also see more pictures and get a bibliography of the site at Perseus' Site Catalog. One of the best pages is found on Dr. J's Illustrated Sites of Greece, where you can find terrific photos and plenty of great commentary to go along with them.
There is plenty to see of archaeological interest too. The most prominent site is the huge classical theater (picture). No one has to pay here, and there are occasional performances infrequently staged (Pausanias 2.20.6). The theater stretches up a very steep hillside and parts of the stage still remain. Many renovations occurred during the Roman period and there are also the remains of a large Roman bath (picture) still standing to its original roof height at places. Mosaics on the floors can be seen and there is even some sarcophagi visible down in a lower level of the bath. Also see if you can find the remnants of the hypocaust heating system below the floors of some rooms. The Argive Agora is not readily accessible (here is the Argive Bouleterion though), but you can wander around the edge of the theater to see some more Roman remains, including a small odeion (picture). If you are in Argos and you have a little time, they also have a very nice, but small, archaeological museum which houses finds from Argos and the nearby site of Lerna. The museum has some great mosaics outside, which have the months (pictured: March and April ) and seasons (pictures: Winter, Summer) personified. Also of note is the krater fragment depicting Odysseus and the Cyclops (picture) - at another exhibition when I was there!! - as well as an 8th cent. B.C. bronze suit of armor (picture).
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