I've been to the mall of emirates yesterday and it was amazing. They have many offers for this Ramadan.
http://www.mymoneysouq.com/financial-blog/top-5-places-to-shop-this-ramadan-in-dubai/ I'm new to Dubai so saw this and went. It was a really wonderful experience.
well it does depend widely on what you are looking for, are you looking for high-end brands or some more affordable items...
1- [url=http://storeleaks.com/blog/2017/06/02/antique-museum-al-quoz/'>The Antique Museum[/url'> is a very good place if you are looking for small gifts, furniture, home decor, souvenirs and such.
2 - The Outlet Mall is a good place if you want to look for more affordable brand products, but you'll need to dig inside stores there.
3- I wouldn't head to Dubai Mall or Mall of the emirates for shopping as they are just too big - dubai mall is generally worth visiting - I would rather go to the lovely mirdif city center I just love it
Hope that helps