Publix is in a class of its own in terms of quality grocery stores.

I often recommend shopping at multiple grocery chains as each tends to have their own specialties.

In LAS, I would recommend

For general packaged groceries: Winco Foods. Recently opened in the LAS area, it's an employee-owned grocery store known for being less expensive than Wal-Mart. Packaged foods are a great value and seasonal produce is generally good. Alcohol is well-priced. Credit cards are not accepted and customers bag their own groceries.

Winco specializes in Bulk foods, many of which are health foods (chia seeds, nuts, fresh ground peanut butter, etc.). Bulk food prices are generally much less than what one sees at other grocery stores.

For meat, produce, and bakery: Von's (Safeway) is the best overall, but some locations are better than others. Prices are competitive if you shop the sales and just the Just4U discounts. Von's also really stands behind the quality of its fresh products. It has a good selection of gift cards and has really been pushing the gas rewards, though it's now starting to assess a $0.10 per gallon charge for credit cards in the form of a cash/debit discount.

Rite Aid and CVS generally have the best beer prices. Trader Joe's is known for its wine selection and Costco and Lee's Discount Liquor seem to be the popular places to buy hard liquor. If you're going to Costco, it also has excellent meats, a legendary wine selection, and has a very long thread in OMNI extolling its virtues.