First off, I am a frequent traveller and a big foodie, and whenever I travel the Chowhound boards have always led to me to delicious food. So now I want to try and give back, for any people visiting Dubai, where I have lived on and off for almost 25 years. Dubai has excellent ethnic food for all budgets from Asia, Africa and Europe, perhaps minus Vietnamese & Cambodian. Please feel free to add below and I can try and edit my post to include suggestions. When I say pricey, I mean anywhere from 100-250 AED per dish. When I say decently priced or mid-level price, I mean below 100 AED (around 75AED) per dish. When I say cheap I mean around 30 AED a dish or less.
Ravi's - Classic Pakistani joint with multiple locations, recommended by most locals. Cheap, original location in Satwa.
Chicken Tikka Inn - Another Dubai classic North Indian restaurant, cheap and not sure of the original location but Ghusais and Jumeirah branch open for quite a long time. Try the classic chicken tandoor tikka (comes as either a leg or a breast) and can request it spicy with some raita (yogurt)
Indego by Vineet - Upscale Indian restaurant by Michelin starred Vineet at the Grosvensor House
Asha's - Personally I find it okay, but lots of people love it. Two locations at last count, one in Mall of the Emirates and I believe one at Al Nasr in Oud Metha. Mid priced.
For Biryani - really hard to recommend since I mostly get it made on order. Maybe try Karachi Darbar for the Pakistani style, cheap. Or really any fairly busy North Indian/Pakistani restaurant should make a decent biryani. Usually quite cheap.
Saranava Bhavan - multiple locations, classic Thalis or Dosas and other South Indian fare.
Bu Qutair - old joint, sits right where the fishing boats come in, little shack by the beach. They only serve fish and shrimp, and they only cook it one way. There is no menu, you just come in and tell them which fish you want or how much shrimp by weight you need (hint: 1kg should be enough for 3 people if only eating shrimp). Recommended, make sure to get the parathas and gravy. Mid-priced
Casa Mia - Classic Italian restaurant once again under the ownership of the original Italian owners. Well-priced, good wine selection, atmosphere and food is generally quite good. At the Le Meridien by the airport.
Bussola - Quite good, Westin Mina Seyahi. Upscale, good atmosphere and nice hotel to boot.
Frankies - Oasis Hotel on JBR Walk, upscale, good lively atmosphere by the bar as time goes on. Owned by Sheikh Mohammed's jockey.
Pizza Pazza - Italian family owned, no alcohol or pork (because not in a hotel), well-priced but have only really get pizzas form there. No pork kinda kills it for me.
Jamie's Italian - Apparently just opened, good food for a good price but have only heard it from friends, have yet to visit.
Asado - Argentinean steakhouse, probably best steaks in the business. Excellent food. Pricey.
Really haven't had steaks in a while in Dubai, but any decent restaurant in a 5 start hotel should be able to give you some good steaks - see also Vu's below. For large groups try Seafire Steakhouse at the Atlantis, but have heard mixed reviews from there. I heard there is another good Argentinean steakhouse opened up in DIFC, but haven't been there yet.
Vu's - Located in Emirates towers, another Dubai classic. Expensive but excellent food, european cuisine (great steaks as well), and on of the highest floors with good views if by the window.
For sushi and sashimi I would say maybe Okku's in Monarch or Zuma's in DIFC is the best, but for fusion I prefer Nobu in the Atlantis. All three are really pricey but the food is quite good. If at Nobu for the first time suggest the black miso cod, the spicy rock shrimp tempura and the jalapeno yellowtail. Other than these three I would say maybe stay away from Japanese food, Dubai isn't really the mecca for Japanese food.
Reflets - Reflets is I believe by a Michelin starred chef, but the food really is exquisite and again really pricey. It's at the Intercontinental Hotel in Festival City. I heard there is another French restaurant opened up in DIFC, but haven't been there yet.
Ton's of good and cheap Lebanese restaurants around, but not really good for fine dining. Can try the classic chains - Automatic Grill & Restaurant (in Jumeirah and on JBR walk), Arz Lebanon (multiple locations). For classic Lebanese style shawarmas I suggest Al Reef Lebanese Bakery (Jumeirah, Karama).
Thai Terrace - No alcohol, but highly recommended in Karama. Been operating for many years. In addition there is Lemongrass (multiple locations) and another Thai restaurant in the Holiday Inn in Barsha in the ground floor which was quite good, can't recall the name.
Again a cuisine probably best explored in other areas, but Noodle House in the Madinat Jumeirah is quite good, and well-priced. When I want Chinese I usually eat here. I hear there is also Hakkasan opened up in Emirates towers.
Istanbul Flower - By the Mazaya Center, quite cheap.
How could I have forgotten the Dubai Brunch! For good food I suggest Spectrum on One is my first choice, followed by Traiteur at Hyatt and Mina Al Qasr I hear is also good. Brunch is usually around 350-450 AED, without unlimited champagne.
There isn't much classic Emirati or local cuisine or restaurants, but depending on where you are I suggest going for Mandi, which is basically a rice dish with chicken and salsa, that is traditional for the region and usually eaten sitting on cushions on the floor, can find in areas like Deira although I hear there is a place opened up in Barsha as well. There is another Mandi place in Jumeirah next to the Chicken Tikke Inn.
Well hope I covered most of it, please let me know if there are any specific things I can help you with! Generally speaking, it is hard to go wrong with food in Dubai, although I would try to stay away from restaurants on the JBR Walk in general, since those are very geared towards tourists and the price to food ratio is really not what it should be. Dubai has amazing food everywhere, just pop into any of the restaurants in the old city and you should find some good eats, enjoy!