Well everyone has their favourite place or somewhere they they well so I am sure you will get lots of recommendations.
I will start by telling you about The Bodrum Peninsular as that is where I have spent most of my time. My parents have been too and they liked Bitez, it is fairly small but not really quiet; there are lots of nice retaurants and a few bars, the beach is nice, it is mainly shingle but there are some sandy parts to along the bay too. The good thing about Bitez is that it is very flat and most of the accomodation is only a few minutes walk from the beach front and most of the restaurants.
It is also very easy to get into Bodrum by dolmus (minibus), it only takes about 15 minutes and there are lots of things to see and do once you get there - shopping, sightseeing, eating out etc.
If it sounds like the sort of plcae they would like and you want to know anything else just ask.
Kedi