Gialos, the port, is a true Greek treasure. Colorful neoclassical mansions flank the hills surrounding the harbor. A prominent clock tower hovers on the western side of the harbor. The upper section of town, Horio (or Chorio) is crowned by the kastro. On the way up the hill, look for the Museum of Symi with archaeological and folklore exhibits. There's a nice mosaic of mermaids at the church of Agios Georgios. Horio has crumbling, winding streets leading to the Knights of St John Kastro where you can see blocks from the ancient acropolis and the Church of Megali Panagia. One of the church bells is made from the nose-cone of a German bomb used to blow up the church in WWII.
In lower Horio, near some derelict windmills is a stone monument, built by the Spartans. The houses of Horio are crammed together, often arching over narrow lanes. You can see neoclassical elements in the doorways and windows. And if you get a peek inside a home, you may glimpse carved woodwork and raised Turkish-style beds.
There's a tiny beach called Nos Beach near the harbor.
A couple of km from Horio is the fishing village Pedi with beaches and tavernas. You can catch a water taxi here that will take you to other island beaches.
To the west of Gialos is Nimborios beach. This long pebbled beach has some shade and umbrellas are available.
Use a water taxi to get to Agios Georgios Bay and the developed Nanou Beach. A boat is also the best way to reach the far west side of the island and Agios Emilianos beach.
Symi's chief attraction, the Moni Taxiarhou Mihail Panormiti (modest dress required) is at Panormitis Bay. This large monastery was first built here in the 5th or 6th Century. The current building is mostly of 18th Century origin. The icon of St Michael appeared miraculously where the monastery now stands. Inside, in addition to the miraculous icon, is a Byzantine museum and a folkloric museum. The monastery is the goal of many pilgrimages since Archangel Michael is a favorite of all Greek sailors, and things can get crowded during certain times of the day.
According to legend, when you ask a favor of St Michael, you must leave an offering in return, so there are many offerings and small gifts. The most interesting probably are the prayers in bottles which have floated miraculously into Panormitis. The bottles contain prayers and money from faithful sailors.