San Diego is where California began, and it doesn't make a fuss about it. The Spanish built a presidio on the hill above Old Town in 1769, which makes it the oldest settled corner of the state. In 1915 the city threw a world's fair in what is now Balboa Park, and the Spanish Revival palaces built for it never came down. Then came the Navy, the tuna fleet and the beaches, and the place settled into the shape it has today: a big, easygoing city with a long coast and a harbor full of gray ships.
It's a very different trip from Los Angeles, a few hours up the coast. The sights are closer together, the traffic is gentler, and you can finish a day with your feet in the Pacific without planning it. Five days lets you do the big three, the Zoo, Balboa Park and the USS Midway, without rushing, and still leave a morning for sea lions and a late afternoon at the tide pools. The honest warnings: the water is cold for most of the year, May and June are often gray ("June Gloom"), and without a car some of the best spots take patience.
The plan keeps each day to one part of town. Day one is Balboa Park and the Zoo with dinner in Little Italy, day two is the USS Midway, the ferry to Coronado and the Gaslamp Quarter, day three is Old Town, Point Loma and Ocean Beach, day four is La Jolla, Torrey Pines and Pacific Beach, and day five is a day trip to the mountain town of Julian. We recommend starting on a Sunday: the free organ concert in Balboa Park is Sunday at 2pm, Julian is calmer on a Thursday than on a weekend, and nothing on the list is closed on a Monday. If you'd rather catch the Saturday market in Little Italy, start on a Saturday and the plan still works. San Diego is also an easy first stop on a longer trip through the United States.