The Ripemarket in Dubai has a nice vibe about it. It kind of feels like you've died and gone to hipster heaven - if it's not hand made, locally sourced, 100% organic, and made of natural ingredients, it's not getting in. Just beyond the stalls were a group of people doing yoga in the park.
Collect a crate and fill your boots with fruit and vegetables wrapped in nice paper bags:
The Miracle Gardens in Dubai are what I describe as a kind of 'Saudi-Gaudi':