My husband and I stayed at The Datai for 8 nights in 1999. It was absolute luxury. Bloody fantastic. Can highly recommend it. We also had 8 nights at Tanjung Rhu which was also fantastic but not as good as The Datai. Nicer beach at Tanjung Rhu though. Both were expensive but worth it.
The Andaman Hotel at Datai Bay is further down the beach from The Datai - we walked through there and it looked ok but not fantastic. Probably not as expensive though either.
We hired a car and drove around Langkawi. If you go into the main town you can buy a few basic foodstuffs, grog which will cut down on your "extras" for food and drink at the Hotels. Both Datai and Tanjung Rhu are quite remote and you have no choice but to eat in the restaurants which aint cheap.
Enjoy>