Another good area for first time backpackers that is close to the Bay Area is the Grouse Lakes roadless area on the
Tahoe National Forest. You reach it using Interstate 80 to the Highway 20 exit, heading west back towards Nevada City for a few miles down into the Bear River canyon, then right (north) on the Bowman Lake road. It has a lot of open granite and lakes, but not a lot of relief, so the hiking is easier. We've done backpacking trips there with small children. It's not an official wilderness area (hopefully will be someday when the local politics change), so there are no permit requirements, except for a California Campfire permit, which you can pick up at any CalFire station (e.g., the one you pass at the Bowman exit in Auburn or the one you pass at the Alta exit). The main lake areas can get crowded, and you might even see a mountain biker occasionally (because the trails are officially open to them, but we rarely see them). But it is an easy place to go without a lot of advance planning. Here are some suggested easy backpacks:
1) The most "mountainy" scenery is starting at the Grouse Ridge Lookout and taking the trail to Glacier Lake. But don't camp there - it's very popular and spots are limited. Instead, continue on the dimmer "use" trail heading north along the ridge to the large lake at the eastern end of Sand Ridge. Better camping there. From that point, you can also pick up a use trail down into the Five Lakes Basin if you have energy for more exploration. To return to the trailhead, take the Sand Ridge trail back to your original Grouse Ridge trail - Sand Ridge has beautiful wildflowers in mid-July and more views.
2) The easiest trail is to start from Carr Lake trailhead and go up past Feeley lake to camp at Island Lake. This is only about 2 miles, so after you setup camp, take a side trip up to Penner Lake. If you are feeling really energetic, walk up the small mountain north of Penner Lake off trail for good views.
3) The least crowded trail would be to start at the Loney Meadow trailhead and head up Texas Creek to the Rock Lakes. The upper Rock Lake is more scenic. This trail has great wildflowers. From upper Rock Lake, you can walk off-trail up to the knobs to the north to look down on Bowman Lake, or to the mountain to the south above Penner Lake for a wide-ranging view.
If you send me a private message, I can send you a topo map of the area with all the trails marked - they are not all on the USGS topo. I've hiked a lot in this area and maintain my own map.