Avoid the two Nakhchivanian "malls." While they are not actual malls to Western standards, they are the closest things there. Instead go to the 57 Bazaar. While the place is run down and a little dingy, you can find the best deals in the city there.
What to buy: You can find televisions, clothes, shoes, toys and food there, pretty much anything.
What to pay: The prices are much lower than in any of the shops around town. For example, as it was approaching winter, I needed a better winter coat. I went to one of the "malls" and the least expensive coat I could find had an asking price of 100 manat (about $110). I went to the 57 Bazaar and found the same coat for 14 manat, and much warmer one for 16 manat, I bought both. You can wheel and deal. Sometimes, depending upon how much the shopkeep has drunk or how badly he is hungover, you can get some sweet deals.