Ephesus is the most amazing European ruins you'll visit (except maybe Pompeii) and must not be missed. Kusadasi is an overdeveloped pit and needs only be seen from the bus windows going out of town. After a morning tour of Ephesus (don't go in the afternoon when it's sweltering), take a long lunch on the ship, book your spa appointment, and enjoy high tea. No need to go into town.
At the port there is a new tourist trap mall that becomes a maze you have to find your way through, showing ID on several occasions, to get back to the ship. The bazaar vendors are extremely aggressive and are best avoided. The city has almost nothing of historical significance. So go to Ephesus in the morning and enjoy the ship in the afternoon.