There is quite a bit of hiking in San Diego. A little driving is a relative terms, so not far how willing you are to drive, but some places of interest:
Palomar Mountain will give you a nice place to hike but will require a drive up Palomar Mountain.
Elfin Forest Reserve has a nice 5 mile or so hike and is Escondido.
I have hiked at the Santa Rosa Plateau which offers some nice moderate hikes and can be pretty in the spring. (north in Murrieta)
If you want a waterfall, want to drive a little, and are in good shape Cedar Creek Falls has a waterfall, but is an upside down hike and is quite a puffer coming back up.
Lake Hodges has many trails that go around the lake, and one moderate trail which will take you to the top of Bernardo Mountain. We were there a few weeks ago watching hawks fly at eye level. On a clear day you can see the ocean. On a not clear day you can see the mountains to the east.
Poway lake (very small no swimming) has a nice three mile trail around the lake. For a more strenous hike it joins up with Mount Woodson which will take you to radio towers and give you a good view of San Diego. On a clear day it will give you a view to the ocean. The lake Poway trail also joins with the Blue Sky reserve which has a nice picnic are a little ways past where the trails join. For a longer hike the Blue Sky reserve will take you to the Ramona Dam. A nice hike until the end where it goes up steeply very quickly.
Remember that San Diego can be hot and dry. Bring lots of water, watch out for rattlesnakes, and in some areas, mountain lions. I have seen neither the snakes or the mountain lions in my hiking, but have seen the paw prints of the lions on some of the trails, and seen many warnings about both.
