One of the finest, The Royal Yacht Club. It is situated next to the water in an upscale neighbourhood. They serve exquisite fare mostly seafood fresh from the sea for prices that are reasonable by Western standards. Service is fast and courteous. Note however that they are not open all afternoon, but only reopens at dinner, so not available for a mid afternoon snack after coming from the beach.
Not far from the Yacht Club, situated behind McDonald's, is a very nice restaurant/bar called "35 Degrees East" Aqaba's longitude, which is open during the afternoon and serves very well prepared Western food including steaks and seafood for prices that are also reasonable by Western standards, though higher than many other restaurants in Jordan. This is also a great place to get a good photo from land of yourself with the famous Aqaba flagpole in the background, without it being obscured by trees.