Because my sons live there, I've been out to San Diego a dozen times in the last 5 years and have spent a fair bit of time hiking in the vicinity.
I agree that Woodson Peak is a fun hike, with the added benefit of its being a short drive from downtown. Just beware of all the antennas and dishes on top.
I highly recommend climbing Cuyamaca Peak, near Julian. It'll take a bit more than an hour to get there, but the area is pristine and the views phenomenal. I'd say it's no more than a 2.5 mile hike to the top. Despite its relative closeness to the ocean, if I recall correctly Cuyamaca Peak is higher than Mt. Washington, though still within the treeline. Don't miss the vast area of grinding holes in the bedrock formed by the Cuyamaca tribe thousands of years ago.
NOTE: signs at the start of the trail warn against hiking solo due to mountain lion danger. I ignored the warning and had no incidents. However, there's a nice teak bench on the trail about halfway up that I rested on on my way down. It was only after I got home that I learned the bench was placed there as a memorial to a woman who was killed by a mountain lion a few years earlier in that very spot!
Joshua Tree is a whole different story, and you can get plenty of information about it online. I loved it there, and would recommend climbing Ryan Mountain - only about a 3 hour round trip but with fantastic views. Be aware, though, that Joshua Tree is a pretty long drive from San Diego (though very scenic) - if I remember correctly it's probably about 4 hours.