There's certainly many beautiful places to enjoy a picnic along the lake, however, your food choices are limited at the lower end of the range. There's no such thing as Tahoe cuisine, unless you head to the casinos for meat and potatoes. That being said, your best bet for picnic fare is a place called Sunshine Bakery on Incline Way. It's a small shop in a mini industrial type park that's owned by an incredibly talented chef making everything from scratch using the best ingredients available. Not a huge selection but everything she does is delicious. It's your only choice.
Another option for lunch with a great view is at your hotel. Across the street from the main building is the Lone Eagle Grill, right on the beach. Great atmoshphere and good food. A little pricey for lunch but ridiculous for dinner. Nice drinks and good lunch selection where you can eat outdoors enjoying the view. Stick to the bar menu.
My favorite inexpensive meal is a place called T's which does mesquite rotisserie chicken, pork, and tri-tip. A little hole in the wall type place that you will thoroughly enjoy. If you like seafood, a restaurant called Wild Alaskan has excellent salmon at a moderate price. They also serve a good yuppie type salad. Grumpy's has decent bar food.
On Thursday evenings, Fredericks has 1/2 price sushi at the bar. Good deal for locals. Otherwise, the cooking is fusion and a little pricey. My favorite high end restaurant here in Incline is Big Water Grille, with nice lake views and great California type cuisine. That's about it for chow in Incline Village. Other recommendations I'll give aren't very far.
If you feel the need to head to south shore and see all the casinos, there's a place called Naked Fish which has as good a sushi as any I've had in Chicago or San Francisco. Can't recommend any other restaurants down there. It's about a 35 minute drive. In Kings Beach(10 minutes) is a terrific little pizza place called Peluso's. Mainly carryout but there is 1 table in front and 2 in back. Thin, crispy crust with homemade sausage.
If you're dying for steak the best place is Open Range in Tahoe Vista(12-15 minutes). There's also a place in Tahoe Vista called Spindleshank that we love to go to for happy hour(5:30-6:30) at the bar. A bunch of appetizers for $5 and 1/2 price wine. Whether it's a special or not, get their roasted artichoke, which is the best I've ever had anywhere, and Oysters Bienzo. I'd recommend driving 1 evening to Squaw Valley. It's really pretty and about a 30 minute drive. A great restaurant is Plumpjack, which is pricey but their bar menu is also excellent with moderate prices. Extremely reasonable wines. Mamasake has good sushi in Squaw, but not quite as good as Naked Fish.
Other restaurants I really like but are probably more than you want to spend are Le Bistro(Incline), Wild Goose(Tahoe Vista), Moody's Bistro, Dragonfly,Cottonwood(Truckee/20-25 minutes). You can check their menues on the internet. You should also find the time to drive to Truckee. It's a very pretty old mining town. Also in Truckee is the Donner Museum, which is pretty interesting(if you know the story of the Donner Party emigrating to California in the 1880"s. You can look it up). You'll have a taste for ribs after seeing the short movie they offer.