The mud baths at Dalyan might be a little far from Turgutries, but there are lots of other lovely places for you to visit on the Bodrum peninsular.
Bodrum itself is a pretty amazing town, well worth a couple of trips (Only about 25mins away on a dolmus). But my favorite place in the world is Gumusluk (15mins). Spend a lazy day there-make sure you take your skorkle, and you should also spend an evening at one of the lovely fish restaraunts, Mimosa is my recommendation