I have spent a lot of time in this area and in the surrounding mountains, which are all so beautiful with so many little lakes to explore.  but if you want a good old easy beach picnic on wonderful lake Tahoe, I love going to pope beach, it's a very long beach and is popular, but if you go to the very end of the long parking area and walk out on the beach, it's beautiful and perfect for a day at the beach, you can even use the bbq pits available.  so, it's not a completely private place, but well worth it and easy to get to, and warm shallow water of tahoe make it perfect for playing in the water.