I have parked at the cruise terminal in San Diego and never had a problem. If you like sea food be sure and eat at Anthony's which is next to the cruise terminal. If you have time you might enjoy Seaport Village which is close to the pier.
There is absolutely no problem parking in the parking lot across the street from the cruise ship terminal. It is secure -- it is inexpensive and you don't have to worry about it at all. We've left our cars there many times for a week at a time and have been very happy having the lot just across the street.
I was just in San Diego last wk. Very near to the airport and cruise port is an area called "Old Town". Anyone there can tell you where it is and what it is. It's a heritage park of the earliest settlement in San Diego. There are old stucco bldgs., & very good restaurants (at a more reasonable cost than you will find in other areas). It's quite colorful, with a Mexican flair. Very clean and pretty & sometimes has music playing in the garden areas. Lots of very nice handicrafts, too. Not just junk. You can visit it in just an hr. for a quick look, or longer if you want to eat. There is free parking in the area and it is free to enter. And as mentioned above, Anthony's is a good place for seafood. There are other, cheaper locations, but the one the writer above is talking about is right on the water downtown. It's rather pricey for dinner (about $25 - $35 per entree) but lunch isn't priced nearly so high. And you can get fish & chips and eat them on a picnic bench right next to it. So, if you can get to the area a couple hrs. before you board your ship, there are some good things you can do.