If you are looking for Dubai garden shops, you should consider driving to this "plant souk" - an area full of nurseries just behind the city borders.
To a fraction of the price which you would pay in the big stores in the city, here you will find every plant you are looking for. Fresh indoor plants are imported weekly from Holland, pots in all colours and shapes are for sale throughout the nurseries, and you can stroll endless aisles of green bushes, cactus, trees and flowers.
The Dubai garden shops in Al Aweer (or Warsan to be precise) also offer home delivery, especially for the bigger plants, and the staff is very friendly and helpful.
Currently there are more than 15 different shops out there, all next to each other.
Interesting things I saw during my visit were animal stone statues for the garden, enourmous painted vases, trees cut in the shapes of elephants, horses and other animals or stone barbeques with a furnace to bake pizza!
To find the area:
is actually not difficult to get there (if you just know where it is
Below information and map should be helpful. It only takes about 20 minutes from Jumeira.
Take Al Khail Road (E44) in direction Hatta/ Oman (If you are coming
on Emirates Road E311, the exit has the same name).
Behind Emirates Road and after passing Dragon Mart and International City, turn right at the next roundabout, following the signs to Dubai Academic City.
Driving on Academic City Road, turn left at the next roundabout. The signs there point to Warsan.
At the next small roundabout you will already see the first shops (picture above).
You can either stop at the first nurseries or explore the ones which lay further behind.
There is no specific nursery which I am recommending here, but the variety is so large that you will certainly find what you are looking for at one of these shops.
Use also Google maps to find the area with the various shops. You can plan your route by typing in your point of departure.