Sometimes forgotten but rarely regretted (!) Corona Heights Park offers hiking (short but exciting!), great views, picnicking, basketball, tennis, a playground and a museum on and around dramatic red rock formations.
For improvised picnics - Courtney's on the corner of 14th and Castro sells excellent fruits and vegetables along with sandwiches and freshly squeezed juices... and is reasonably priced by SF corner store standards :)
Otherwise, nearby Buena Vista Park has better trails and more wind protection for those seeking slightly more accommodating terrain.
Address: Corona Heights Park, SF
Website: http://en.wikipedia.org/wiki/Corona_Heights_Park