The diamond district is a great place, but also a great place for people with egos to get ripped off. Most people who know something (but not enough) about diamonds assume that... Say, a GIA 1 ct G SI1 Triple Ex cut round diamond... is the same as any other GIA 1 ct G SI1 Triple Ex round, and they compare prices by certificates. That is just so insane. I work in diamond wholesale and I wouldn't ever consider doing that. Two diamonds with exactly the same specs will be traded (internally) and sold (externally) for different prices. Because every diamond is unique, and when one is better it costs more.
Honestly, for most people without a friend in the industry, independent retail stores are the way to go. Shop around. Ask for a discount, and negotiate. And make sure you look at the diamonds, not the certificates. There are great deals to be had (like my company, but I won't name drop here as that wouldn't be appropriate) but ultimately if you go out on your own I would recommend to anyone to be humble about it and be willing to spend a little more to get a better diamond (of any grade).