I saw a question about this on the alainexpats yahoo list. (See my Links page for more info about this.)
Here’s how I replied…
There are lots of places that do this.
We live behind the Hilton, so there are several places there.
If you were to come out of the Hilton, and turn right at the roundabout, going across the bridge with the 3 Sheiks pictured, go across the lights, and take the turning on the right which enables you to park in front of Lulu Kuwaitat. Looking north at Lulu walk 10 metres east onto the north/south road. Turn right.
On your right-hand side you’ll find a typing shop.
They will fill cartridges while you wait.
If you walk 20 metres further south you’ll see steps down into an underground shopping area with a couple of computer shops and other workshops. One of those fill cartridges there and then.
I think I paid about 5 aed to fill a black HP cartridge and maybe 10 to fill a colour one.