Symi town gets extremely crowded in season with visitors, both day trippers and those staying longer, and even in shoulder season it can be difficult to find accommodation on weekends and holidays without advance booking.
One well established travel agency that can help with finding accommodations is Kalodoukas Holidays (http://www.kalodoukas.gr/), 85600 Symi, Dodecanese, Hellas. Tel: +30 2246 0 71077, fax: +30 2246 0 71491, mobile: 6948808011 email [email protected]. They can also handle other travel activities like cruises and boat rental. They have an office near the harbor inquire locally for directions.
Symi is full of characterful villas and houses. You can stay in a restored house in the old town, Chorio, but you'll need to climb the numerous steps to get back and forth to the harbor, and it will take some time to learn how to find your apartment in the maze of streets and alleyways. Or you can opt for harbour side views in Yialos. There is also accommodation in the quiet beach villages of Pedi and Nimborio.