Welcome. You even spelled Sierra correctly without an s at the end!
From San Diego you may want to head to Joshua Tree. Tons of world class rock climbing and a good chance of good climbing weather. It's mostly single pitch stuff, so don't expect big mountains.
From SoCal you'll head up highway 395 to "the Eastside". The eastern slope of the Sierra. TONS of world class climbing and skiing here. Hopefully we'll get some more snow though because we haven't had any since December. Bishop is the main town in the area. An hour south is Lone Pine and the road to Mt. Whitney. An hour north is The town of Mammoth Lakes and Mammoth Mountain a great ski resort. Near Mammoth Wild Willy's hot springs is super fun. Owens River Gorge is the most extensive sport climbing area in California, and is climbable year round, weather permitting. Tons of backcountry skiing and other climbing options (though many may be snowed in) in the Eastside.
In the summer you can cut over the summit 30 minutes north of Mammoth from Lee Vining through Tuolumne Meadows to Yosemite Valley, but it's closed in the winter due to snow. So you'll need to go north for a few hours, then cut west by Lake Tahoe. Lots of skiing options in Tahoe (Mt. Tallac is a classic/popular backcountry ski peak) and possibly rock climbing, weather dependent (e.g. Sugarloaf off of Highway 50).
From Tahoe it's about 5 hours to Yosemite Valley. Which as a rock climber is a pilgrimage everyone should make. South facing walls/crags may be climbable weather permitting. Even if you don't climb on El Cap hike to the climb Pine Line at the base of the Nose, put your hands on it, and feel the energy.