Vancouver:
Jericho beach-ish area. At the Jericho Sailing Centre, there is a casual dining place called "The Galley Patio & Grill"
where they serve amazing burgers made with Angus beef. There are also options for vegetarians as well. You can eat on the patio and admire the view of the beach/ocean, a few steps from you. I know it kind of defeats the idea of a "picnic" but you can always order and take it to the beach.
Point-Grey Foreshore:
After Jericho, you can walk along point grey road until you hit the Point Grey foreshore at around Dunbar and Point Grey. I used to live in a basement suite around there, and on mornings I'd take my breakfast coffee down to the foreshore, climb down these slightly hidden long flight of stairs down to the foreshore beach and walk along the beach while the tide is low. It's a natural beach so you'll see starfish clinging on to rocks and crabs scattering about. The best part is that you see this amazing panoramic view of Downtown Vancouver from there. On a clear day, it's stunning. I don't think many people visit this beach either.