Reno has several good spots to fill your picnic basket with interesting foods. My first stop would be Wild Oats Market at 5695 S. Virginia. Prices are a little on the high side, but the variety and quality can't be beat. They have an in-house sushi chef, an extensive deli department, and more exotic cheeses than you'll find probably anywhere else in Reno. There is also a bakery for your bread and dessert. It's an organic market, so you'll also find a large selection of juices and fresh fruit.
My next stop would be Trader Joe's at 5035 S. McCarran. Trader Joe's is less expensive than Wild Oats, but also has an excellent selection of cheeses and fresh picnic goodies. You'll also find wine at very reasonable prices and some unusual soft drinks and juices. If you didn't buy your bread at Wild Oats, Trader Joe's can fill that need, too. They have packaged breads as well as the wonderful Truckee Sourdough (at about half the price you'll find it in local supermarkets). They also have some unusual snacks (like wasabi-dusted fried peas, blue corn tortilla chips and peanut butter-filled pretzels). There is also a vast selection of cookies and chocolates for your picnic dessert.
If you haven't found a wine to your liking, head over to Cost Plus World Marketplace at 4987 S. Virginia, where they also have a variety of wines from around the world. And you can even buy your picnic basket there! Bon appetit!