Turtle Bay at Daylan is beautiful, if you stay in Fethiye there's a daily boat trip which goes there. As above, well worth a look.
Olu Deniz is also lovely. Lots to see and do, especially if you're into watersports. Not my cup of tea, but it appeals to a lot of people.
Yalikavak is a small fishing town located on the Aegean coast. Aside from the fact my parents have a house here (which incidentally is available to rent) ;) it is absolutely gorgeous and far less developed than many of the 'popular' tourist areas. Lots of lovely restaurants, a market every Thursday which is a must, and a beautiful beach. There's no loud bars and clubs (yet!) and they've also got a huge amphitheatre where they hold lots of events and 'entertainment'. It's lovely to sit beside the harbour and watch the fireworks go off at night :)
I've posted loads of pics on TripAdvisor, both of the house and the area, so maybe have a look on there for an idea, and other people's recommendations.
If you don't like bars and loud places (I don't either) then I would stay away from places like Marmaris and Altinkum. Horrible places, and it'll take you half an hour just to get past all the locals trying to sell you trips!
If you do go to Turkey, then be sure to take a trip to Pamukkale and Myndos Gate. Lots of other historic sights, check them out before you go and plan your trip to ensure you get the most out of it.
Have a great time :-)