My husband just got back from Dubai so this is second-hand-but here goes.
The first night in Dubai he and a colleague went to Bastiakah Nights, a restaurant in the old section of town. Apaprently it's built in an old riadh, around a very pretty central courtyard. It's a prix fixe meal that started off a cream of barley soup, which he was delightful; then a platter of seven different kinds of appetizers, inclduing an eggplant dish he really liked. You can choose your main-he picked a lamb that he said was exceptional, and dessert was really nice as well-a selection of very nice fruit, tea, cookies and pastries. It ran about 50 euro/person. I think the setting was really enjoyable from what he said, and the service quite nice as well.
Here's the website if anyone wants to check it out sometime.