the big bus tour seems to hit all of the shopping malls, which i find fashionably boring. but then again, what's to do here in dubai but shop?
i've used the arabian adventures for their desert safaris and while it was great fun, they tend to be on the pricier side. try net tours- their safaris are just as good. also, i found that if you call them, you can haggle the price. i got a 60% discount last time... of course they didnt want to give it, but if you persist they'll eventually cave in.
and some advice on the safari, don't sit in the back seat. i'm talking about the very back. you'll get thrown around and likely to get motion sickness.
good luck and have fun. you'll be here for DSF so prepare to shop!