Al Fahidi Street - Either side of the Creek, the heart of Dubai, there are two of the older shopping areas - around Al Fahidi Street in Bur Dubai and between the gold souk & Naif Road in Deira. I prefer them to the ultra-modern shopping malls, the atmosphere is so much better, and there are plenty of bargains to be had, whatever you're buying. They are also much better than Karama, which is much over-hyped and is a soul-less, boring area to walk around. Al Fahidi Street runs parallel to the Creek, just walk up to it through the side streets. Explore them too, they're fascinating and perfectly safe to wander around.