Dubai just got its Michelin guide in June so that would be a good starting point for your search. In general the upscale restaurants I've visited here tend to be more party / entertainment-oriented as opposed to the more formal places you'd find in Europe (for eg. Amazonico, Mimi Kakushi, Coya, Gaia, etc.).
You also have the UAE branches of Zuma, Cipriani and Il Ristorante by Niko Romito (both the Milan and Dubai locations are Michelin-starred and are in their city's respective Bulgari hotels).
Such restaurants tend to either be in the five-star hotels or in DIFC (DIFC being quite close to the airport). If looking for something nice but more regional, there's Ninive in the Emirates Towers which serves a pan Middle-eastern / North African menu and Orfali Bros which does excellent, innovative Middle-Eastern fusion but is mostly casual.
Ro