I visited San Diego in 1995 and again in 1997.
It was one of my favourite stops while backpacking the USA.
Really, it depends on what sort of things interest you.
For me, I loved Balboa Park with its Prada (the main street) with its beautiful architecture lining the street, you have San Diego Zoo, and the Museums. The Science Museum with its hands-on exhibits was fun. All these were in the same park. Elsewhere you can visit the Sea World with all its marine life. I fed the dolphins, I watched them perform, I watched the killer whale perform - and got thoroughlly soaked. There are sharks, moray eels penguins and many other lifeforms on show. There is even a tower from the top you get a panorama of the entire attraction as well as the Pacific Coast. And you are never short of cafes and resturants.
Mission Beach north of the city is worth visiting, I believe now linked to the city by the Trolley Tram system, which also takes you to the Mexican border. From there I spent a day at Tiguana (bring your passport for this).
Finally, the Old City, also linked by the Trolley Tram, is full of working, hands on exhibits of the Wild West, along with the Bazzar which had a band stage.
In the city itself, the Gaslamp District may be worth walking through.
I stayed at the AYHA Downtown Backpackers Hostel in Market Street. But first enquire whether they'll accept American visitors, since in my day they only accepted foreign tourists.