Yes, it is very family friendly. It helps if you kid can tolerate psych-rock. And you can tolerate funky beers.
oh I love the funky stuff...don't think anyone else will
but I can them there for a beer and a growler fill 
Old Rag is the nearby hike I always do. I took my then eight year old last Spring. It was quite challenging for her, but she had a blast rock scrambling. Probably not a good choice unless you've done some other shorter hikes with the kids, or unless the kids are older.
White Oak Canyon is another hiking favorite.
kids 7 and 10 are pretty nimble, taken them on the Billy goat trail
not sure if that compares in difficulty
I've seen seven year olds on the Old Rag hike, but I know mine wasn't ready for it at that age. Whe was nearly 9.
Old Rag is harder than Billy Goat Trail. For three reasons.
1. There's a huge amount of elevation gain before you even get to the rock scrambling. 2400+ feet in all.
2. It's longer. 9.1 miles if you take the loop, 7.4 miles if you do the up and back.
3. The rock scrambling is marginally harder....My kid is tall/long limbed for her age (gets it from mom, certainly not from me), so that helped.
White Oak Canyon is good because you start by hiking down. And it's a down and up hike. So you can turn around at any point. Nice if you can make it to the first waterfall though, good place to picnic.
This all reminds me, national parks are free on Monday. In honor of Lincoln, FDR, and Obama.
