Oooo this is going to make me hungry and sad... lived there for 4 years.
Ravis - best curries ever, dirt cheap, plastic everything, absolute opposite of Dubai glamour and you have to sit in Satwa traffic to get there. Still the place I miss the most.
Nobu - absolute opposite end of the scale from Ravis but to die for food. But very very pricey.
Elevation burger - dirty hangover burger (though even GBK is inifinitely tastier in Dubai and tend to be more convenient).
Claw (Souq al Bahar) - brilliant for a booze up with a group. The swamp dip is amazing and strawberry daquiris and prawn enchiladas yum yum!
You absolutely have to see the fountain show between Souq al Bahar and Dubai Mall. My best tip is to book a table (well in advance) on a terrace at one of the Souq al Bahar restaurants (Dubai Mall side doesn't serve alcohol). This way you get to see a few shows (I think they are every 30 mins from 7pm). I used to love Karma Kafe and at the time if you went on a Tuesday it was Ladies night and you got free drinks and massive discounts on food. I think the MeatCo also had fountain views on their terrace if that is more your thing but call to check.
Aprons & Hammers (the one on the boat at the Marina next to Barasti is the best) for a bucket of crab.
You must must must do a Friday brunch. They are everywhere but they are not all equal. It also depends on what you like (i.e. preference for top quality food vs party atmopshere or somewhere in between).
Most people do a brunch on Christmas Day.
I have just read you are a fussy eater though whereas food is my favourite thing in the world so I am probably the worst person for advice.
Definitely the fountains though! I've seen them gazillions of times and they still make me emotional.