Rue Neuve is the place to go shopping if you are in the mood to shop. It has stores upon stores of everything, from mobile phone stores to shoe stores to clothes and perfume shops. I would suggest you go down this street even if you aren’t looking to buy. It has some very chic and high-end places to shop at and can be an experience even if you are "just looking."
The best time to visit Rue Neuve is in January. I know it’s not exactly the middle of tourist season, but if you are here at that time, you hit the sales! The sales are huge, and you can get a new wardrobe for a fraction of what it would cost any other time. An example of this is when I bought a pair of pants for 5€ that were originally 65€! How can you beat that? The price was so good that I had to buy my sister a pair as well, plus they are one-of-a-kind, so there is always a good story there.
If you are interested in looking at a large department store, I would check out INNO. It has everything from drugstore cosmetics to designer bags. I found some great deals on accessories here and bought a ton of patterned nylons and scarves (they were the best prices around). Also, Clinique is made in Belgium, so if you are a fan of this cosmetic’s brand, I would suggest stocking up.
Rue Neuve is a street with numerous other shops besides simply INNO. It also has H+M (they have three separate shops); Zara, a slightly more upscale H+M; Etan; Benetton; shoes stores galore; cosmetic stores; and places for luggage. I found a great deal on a large duffel bag that I bought in order to bring home all the new stuff I acquired after being in Europe for 6 months.
Rue Neuve also has City Mall 2, which, I believe, is only one of several "malls" in Belgium. It is interesting to go there just to see the difference between the American concept of a mall and the Belgian one.
While Rue Neuve is nothing particularly Belgian, it has European fashions if you are looking for them. This is where you will find the clothes that everyday Europeans are wearing that will make you distinct in the US. Plus, if you go in January, you can’t beat the prices.