Molto Vegas Farmer's Market: This farmer's market created by super chef Mario Batali is by far the best in town. You can get gorgeous mushrooms for a fraction of the price of Whole Foods, as well as all kinds of other interesting produce and locally grown foods. The downside is that it is only open from 11-1 on Thursdays and it's located in a warehouse on the far South side of town: 7485 Dean Martin Drive, Suite #106.
Sieu Thi Thuan Phat: A great Asian market in the Southeast corner of Spring Mountain and Decatur. It is very clean and they have tons of fresh produce and fish. If you want to prepare an Asian dish, this is a great place to get your ingredients - they even have pre-shredded and pounded green papaya to make Thai papaya salad, one of my favorites. Wild Chilean Sea Bass is $9.99/lb and red bell peppers are $0.99/lb.
Nakata Market: A small market with everything you need to make sushi, udon, or other Japanese dishes. They have everything from DVD's to chopsticks, with several aisles of food in between. Be sure to get Kewpie mayonaise, which comes in a soft plastic bottle packaged in a plastic wrap and has a cartoon baby on front. It will replace the mayo you usually use and is wonderful in creamy salad dressings.
Valley Cheese and Wine: This great little shop is out of the way for most people (located on Horizon Ridge and Valle Verde), but it is definitely the best place to shop for cheeses and cured meats in Las Vegas. The owners are helpful and the selection is vast. They recently added "to go" farm baskets full of organic vegetables so you can get almost everything you need for a dinner right here.
The International Marketplace: This is a great one stop shop to get all your needs for cooking almost every kind of cuisine you can imagine. 5000 S Decatur Blvd.
Parma: The perfect place to pick up a wonderful and fast pasta dinner you can prepare at home. All the fresh pastas are made in house and you can buy their sauces as well. They also have a nice deli with various salumi.
Cardenas: This is a fabulous new Mexican market with great meat selections, beautiful and affordable produce, house made tortillas and chips, as well as unique items. Additionally, the shopping experience is much better than at another popular Mexican mega-market, Marianas.