If you want an authentic Thai drink, try the super-sweet Thai-style ice-tea which you can order with milk (cha yen sai nom) or without (Cha dam yen).
The food served is very tasty and even the pickiest of eaters (including the childen) should enjoy a plate of Khao Man Gai. The restaurant staff can help you with which sauces to put on though only a little is needed as it is quite spicy and salty.
Pee Daeng's Restaurant is located just opposite the large "Fisherman's Village" sign in Bophut and is generally open from around 11am to around 5pm each day. Though they do seem to be closed a lot and there doesn't seem to be any set days of closing, so you'll just have to leave it up to luck as to whether the restaurant is open or not. If not, chances are it will be open the next day.
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