OK, here are some ideas off the Interstate 80 corridor, all within two hours of Sacramento. These should all be open by late June or early July. Check the Tahoe National Forest website for road and campground opening dates.
1) Grouse Lakes roadless area - take the Highway 20 exit from I-80 westbound back towards Nevada City, drive down the grade about 5 miles and turn right on the Bowman Lake road. This is a paved road. Follow it through Bear Valley, across the South Fork Yuba River, up past Fuller Lake (lots of local fishermen there since they stock it). In the next 10 miles you will pass connections with gravel roads to several primitive camp sites and trailheads. The best ones (in my opinion, of course) are found in this order as you drive on the main road:
a) Grouse Ridge - the road goes several miles, some of it washboarded but all passable to a normal car, up onto Grouse Ridge. There is a primitive campground and then a main trailhead for day hikes or backpacking into the Grouse Ridge area. This Caltopo map view with the open street map overlay shows the trails:
http://caltopo.com/map.html#ll=39.40045 ... &b=t&a=mba
Not shown are easy use trails and cross-country routes down and around the Five Lakes Basin from the big lake at the east end of Sand Ridge.
b) Carr Lake - there is a big parking area just before the lake. There is a walk-in campground at Carr Lake. An easy hike continues on past Feeley Lake to Island Lake and then up past the Crooked Lakes to Penner Lake. This is a great area for easy backpack trips with children.
c) Loney Meadow - no campground, but a great hike past the meadow (lots of wildflowers early to mid season) and then up along Texas Creek to the Rock Lakes. The lower part of this trail is not shown on the caltopo map link above, but is easy to follow. Rock Lakes make a good short backpack trip. I like the upper one better - campsites along the west shore. Easy climb from there up to Peak 7264 to the south for good views.
2) Castle Peak roadless area - take the Castle Peak/Boreal ski area exit from I-80 just before Donner Summit, go to the north side of the freeway, and then up the short paved spur to a big parking area where the road turns to dirt. You can continue about 1/2 mile on this rough road, even with a normal car (if you drive carefully) past several informal dispersed camping spots - bring your own water or purify creek water. Then there are great hikes up the road to its end and beyond on the PCT or up to Castle Peak on a use trail. See this caltopo link:
http://caltopo.com/map.html#ll=39.36217 ... &b=t&a=mba
3) Donner Pass Pacific Crest Trailhead - take the Soda Springs exit off I-80 and head east to Donner Pass. Just before the pass, there is a minor road heading south (probably signed for Lake Mary). After a couple hundred yards, where it bends, there is a Pacific Crest trailhead. Park in wide spots along the road. No camping here, but great day hikes or backpacks up the PCT. For a good dayhike loop, we like to head south up the PCT and then do the Mount Judah loop. Just scroll down from the caltopo Castle Peak link above to see these trails.
There's more, of course, but this should get you started. Study the map and explore. Oh - here's a suggestion - skip the Loch Leven trail from Big Bend off I-80. You hear freeway noise the whole way and the trail is badly rutted. Instead, find the "back side" trailhead by Huysink Lake, coming in on good Forest Service gravel roads from Lake Valley Reservoir, which you get to from the Yuba Gap exit on I-80.
-Phil