The outlet mall has some fantastic sales on beachwear, I bought four bikinis last week, Billabong & Ripcurl from as little as 55 AED and they have other beachwear also.
BHS(but in Abu Dhabi) had some lovely sarongs and on sale right now. The swimwear/bikini's werent so nice. Think they were about 50-60 dirhams, hope you find Dubai stores have them on sale aswell