Al Fanar Restaurant offers local Emirati cuisine and the restaurant's atmosphere is designed to capture the feeling of traditional local culture. The name "Al Fanar" means "lantern" (often of the color blue). There are two Al Fanar restaurant in Dubai and one in Abu Dhabi. Many of the dishes are delicious and many of my local friends enjoy a lunch or dinner here on weekends. 

A lunch at Tom & Serge in Dubai is always a good idea. The food is great and the service good. It is however a bit crowded and loud, but if you can handle the atmosphere of a popular restaurant then you will for sure have a good time here.

At Bu Qtair you will always be served excellent fresh fish and seafood. It is a very simple eatery, actually just a shed. But don't let that fool you and turn around. They open around 6pm and is often crowded - first-come, first-served basis. The location is relatively close to Kite Beach, map. 

Friday + cool weather (20-30 degrees) means Ripe Food & Craft Market in Zabeel Park, Dubai. You can roam around numerous of local farmer stands with locally produced vegetables and organic choices, start-up food/restaurant companies, as well as some established eateries.
You might also come across a few arts and craft stands with photography, artwork and jewelry - as well as a couple of troubadours.
It's open between 9-14, only on Fridays.

I'm testing the traditional ornaments

Pretty jar (of fat)

Safa Part is one of a few man-made oasis. The part is also the home to a "library café", The Archive Café, which has great desserts and enjoyable atmosphere.
Safa Park is also the home to numerous markets during the weekends, such as the Ripe Market (sometimes in Zabeel Park), "Market of Everything" and flea markets. 

(Photo from The Archive's website)