Of the big three, there's also San Jacinto and surrounding peaks.
Some less visited but interesting hikes that can get a little more fun in the 2nd class department would be the Yucaipa ridge peaks, particulary Galena peak via the headwall. You don't need permits since it's just outside the San G wilderness, and travel is almost completely cross country. For anyone comfortable with general mountaineering, this hike is no sweat, but the headwall has been known to defeat more casual hikers (mostly out of fear).
Outside of that, Baldy is an hour from Hollywood, and you could do the Bear Canyon/Village trail, which is about 6,000 ft. g/l in 12 miles R/T, or the classic fallback ski hut trail, but that'll fall under your 10 mile minimum.
If you really want to minimize driving, don't care about how high you go but just want 4,000 ft. plus g/l, you could look at Mt. Wilson via the old trail, or Mt. Lowe from Altadena; both will net you over 5,000 ft. g/l (low summits though), and over 10 miles hiking; close to 15 for Wilson. You could also go past Lowe and keep going to Markham and San Gabriel.