Take the bus for half an hour into Bodrum itself and you will find 3,000 years of history. Look around to see the ancient Mausoleum of Halicarnassus, the preserved Myndos Gate where Alexander the Great forced his way into the city, the ancient Greek theatre, or the Crusader Castle built with the remains of the Mausoleum. There are also dozens of narrow streets stuffed with interesting shops and cafes.
The ancient city of Ephesus is within reach for a day trip. Coach excursions are available from the hotel. Enter the site and step back in time to the height of the Roman Empire. In its heyday, Ephesus was a great trading city, one of the four great cities of the Roman Empire, rivalling Alexandria, Antioch, and even Rome itself. You will see the main buildings of the city, mostly from the second century AD, with monuments to the Emperors Trajan and Hadrian. Other sights include the Library of Celsus, the main agoras, and of course the great theatre which features in the Book of Acts in the Bible.
In its golden period, Miletus was a significant port although now it is many miles from the coast. Although not as extensive as Ephesus, the archaeological site is fascinating and includes a substantial theatre and a bath house.
The temple at Didyma appears not to have ever been finished. It was built to contain an oracle and seems to have been built outside any town as there are no other remains around it. The speculation is that as Christianity spread across the Roman Empire, so the demand for its particular brand of fortune telling dried up and it was abandoned.
Take a tour to the mud spas of Dalyan. Enjoy a boat trip down the Dalyan river and then experience the therapeutic mud baths in the spa.
Lasos was a small Roman town, now just a fishing village on a small cove. It's hardly ever visited by tourists, which means if you have ever wanted to wander round a Roman town by yourself, instead of fighting through the crowds as you do at Ephesus, then come to Lasos. It's a charming site on a small scale.