Don't eat,drink in public, there are CCTV cameras in the city.
These are some restaurant that are open all day during ramadan in Dubai. Tried these by myself.
Cafe di casa
Located just beside gold and diamond park. FGB or First Gulf Bank Metro Station, they have the most italian food especially pasta.
25 55 Cafe Bistro
Located at Dubai Marina Yacht Club. A few steps from jumeira lakes tower metro station. Pass through the small children playground and its there.
Located at the ***** IBN Battuta Movènpeck Hotel.
They have international buffet breakfast during ramadan. Great fresh food selection.
After breakfast you can go to the temperature controlled swimming pool and be served with a food there too.
Dubai International Financial Center
All the restaurant at The DIFC are open for dining from lunch to dinner. I ate at Noodle House beside the SuahiArt which is also open. Caribou, Potbelly, Gloria Jeans etc. DIFC is a financial and commercial center that is located just a few walks from the DIFC metro station. Most of the diner here are office worker.
If you are a tourist or a resident who are strolling in Dubai during daytime of Ramadan, the biggest challenge you are going to encounter is finding a restaurant to eat when you get hungry. Most of the restaurant are closed in the daytime and opening in the iftar which is around six to seven o'clock in the night.
Some coffee shops, restaurant are open but they are just open for take away and delivery orders. Never try to eat food or chew anything in public because you might be in a serious trouble they might put you in jail.
Where to eat as much as you want.
Well.. most of the restaurant that are inside the hotels are open, and they are open not just for in-house guest, mostly are open for public. They serve the normal menu just like the ordinary days. They even have a buffet so you still can enjoy your breakfast and lunch. If you are worried about the price, well don't expect hotel food prices to be like KFC or MC Donald. Prices in a hotels restaurant are ranging from from 50 Dirhams single meal to 200 Dirhams. That is from ordinary to luxury hotels restaurant.
Most of the Shopping Mall Food Counters are also open for take away orders, you can order take away and eat it in the toilet and make sure no one see you because they might laugh at you or to the worst they might complain you.
The point is to respect the people, the culture, the religion of the United Arab Emirates.