Uggs aren't really much cheaper here than in the UK so not really worth it.
Abercrombie & Fitch is hugely cheaper if you like that sort of thing. As is Hollister. A&F jeans are really good and there are often good deals on them. (I will be stocking up before we move home) - Depending on the age of your kids - A&F kids is also massively cheaper here.
Kate Spade if you can get it - definitely cheaper, but if he can find an outlet mall even better. (I got a gorgeous bag a few months ago for $90 - about £55!)
Same goes for Coach.
If make up is your thing, then yes - Sephora is good.
High end denim is cheaper here if it is a US brand - not so much with European brands - things like Diesel are really hard to find and are often more expensive than at home.
Macy's is a good department store to get bargains in - they ALWAYS have a sale of some sort. Brands like Hilfiger, RL, CK are cheaper in there and they have loads of variety. Also good for some watches. (We got our kids ICE watches for christmas for the equivalent of about £25 each.)
Nordstrom is a higher end department store, but you won't get so many bargains in there.
For shoes Macy's is great. If you wear casual shoes then TOMS and Converse are a lot cheaper here - both for adults and kids - just watch on sizing as US sizes are different.