http://www.empostuae.com/Courier/ourLocations.html#a_1
I visited this PO once years ago and it is closer to Sharjah than Dubai! The map on the website is terrible, I would suggest getting the metro to somewhere close (Union Square probabaly) by and then jumping into a taxi!
The nearest metro is, I am assuming, the one at the Deira City Center. Nearby, there are abaya shops, cafeterias, etc. There is a library right next to it. The Abu Hail Center and the Century Mall are also close by but I'd say nothing is in walking distance in this heat.