The sum total wisdom of a variety of guidebooks seems to be that Mission Beach is the official 'coolest' place to hang out in San Diego. We hung out here for part of an afternoon and found it to be a nice enough beach (as beaches go). People watching here is fairly interesting except it's hard to find a nice out of the way café to do that at.
A bit farther south is Cabrillo national monument. This is a spit of land that sticks out into the Pacific ocean opposite downtown San Diego. On the west side of the peninsula is a rugged coastline where tidepools are the popular attraction. We also saw seals swimming off the coast here (or maybe sea lions, who can really tell at that distance).
The east side of the peninsula faces the city of San Diego and the huge (mostly) natural harbor. The pleasure boat traffic is really quite amazingly high in and out of the city. There's also a fairly good view of the northern Baja coast from here.
Cabrillo comes from Juan Cabrillo who landed hereabouts in 1542, and this is his rather ornate monument found inside the park. The next part of San Diego to develop was the area now known as 'old town' which was sort of an colonial Mexican settlement which has now turned into a modern Mexican tourist mecca. We found it a good spot to have a margarita in.
You don't have to visit the San Diego Zoo when you visit San Diego, but it seems somehow like sacrilege not to. We visited both the zoo and its enormous extension northeast of the city, the San Diego wild animal park.
I wouldn't say it was far and away the 'best' zoo we've visited, but it's certainly a good zoo. A bit hilly, so a full day of walking around can get rather tiring but where else can you watch red river hogs frolic?
The modern nightlife district of San Diego is the gaslamp quarter which is a surprisingly lively area downtown. There's not a whole lot to do here other than eat (and drink), and maybe a small amount of shopping if one is so inclined. We just ate (and drank).