Not from Ixia but from Mandraki Harbour in Rhodes Town which is a short taxi ride away.
Don't have current prices but it's alwys cheaper to book directly at the harbour rather than through a rep/ travel office.
Lindos by boat is very popular as they often stop en route for a swim, which is fun and the day trip to Symi is v pleasant (a nearby island with a picturesque town selling sponges and spice).
You can also visit Kos or Marmaris (Turkey) for a day by hydrofoil.

Also Thiros and Nissiros are supposed to be good trips but haven't done those myself. Next time----maybe!!