The town is great for shopping at less touristic prices - try bartering for a real bargain in leather, ceramics, gold and spices here.
In the centre of town you'll come across sarcophagi just sitting in the middle of the pavement! (as in this pic). This one is just by the Fethiye Archaeological Museum - we didn't go in but artefacts can be seen from the Lycian, Roman and Byzantine eras.
I find it a little strange but there are a lot of sarcophagus lying everywhere all over the town of Fethiye -- some in small parks, an ordinary neighborhood street and I saw one sitting right in the middle of a clean road.
Some in really intact and good condition but some already fallen apart, walk around the town, you'll definitely spot several of them.
The big sarcophagus near the governorate's building is well placed and with complete information.