Visit the Eupalinus Tunnel.
It is located at Pythagorio.
How to go there?
If you are coming from Samos Capital to Pythagorio at about 8 km you will See at Pythagorio a sign that tells <to monastery Spiliany> and <Eupalinus Tunnel> at your right. Follow the road to go to the tunnel. In the tunnel. The water was channeled through pipes which were instaled in the acqueduct below the part of the tunnel in the direction of the source and along-side it in the direction of the town. The length of the tunnel is around 1046m. The section of the tunnel is on average 1.80m and it cuts through the mountain at a depth of 180m.The greatest project commissioned by polycrates in the 2nd half of the 6th century BC was the aqueduct for the ancient city of Samos, known as the Tunnel of Eupalinos. This projectwas a duct which was constructed to carry water from nothern side of the acropolis to the south, near the city. In order for this project to be carried out, the engineer Eupalinos of Megara was summoned. He made all his measurements and calculations externally on the surface of the hill before opening the tunnel which measured 1,046m in length. The excavation was done by two seperate parties of workers who dug paralel to each other from the north and south sides and managed to meet in the middle with only a minor deviation. This project was justly regarded as one of great engineering achievements in antiquity!

Visit the temple of Hera
It is located at Iraion.
How to go there?
It is about 6.6km from Pythagorio. 1.7 km from Pythagorio you will see some traffic light posts. You must turn left at the direction of the airport. Don't turn at the airport but keep going. At 4.5 km you have to turn left (there will be a sign). In front of you, you will see the temple. You must have time there because the whole thing is huge. You can see the ancient roads, the great column of the temple, some great statues.
History. In the time of the tyrant Polycrates. Work began on the building of a new temple measuring 55.16 x 108.63m, with 155 columns of aheight of approximately 20m which however, was never completed, because of the political and economic collapse which followed the death of Polycrates. The 3rd and 2nd centuries Romans carried off many statues from the site. however, the Emperor Augustus was favourably disposed towards the island and gave its people the privilege of beeing Roman citizens.