Rancho San Antonio County Park offers good hiking and trail running. Several challenging trails through this park lead to Black Mountain, whose summit is located in adjacent Monte Bello Open Space Preserve.
The trails are heavily trafficked during the weekends. Parking is also a challenge if you don't arrive early enough (before or around sunrise). I had an Asian woman behind me on the trail and she kept on Facetime-ing, loudly, for a good 10-15 minutes before I finally managed to shake her off by picking up the pace.
The trails are dusty, but shaded almost 50% of the way. Change in elevation can be pretty steep for some, but the views from vantage points at the top are pretty amazing. Overall, the landscape is all about the undulating hills, the flora and a few deers representing fauna.
Do put on sunscreen and feel free to ditch your hiking shoes/boots for something as light as a running shoe.