The Lake Tahoe Basin and surrounding region covers a vast expanse of the northern Sierra Nevada and holds a lifetime of climbing, mostly on fine-grained, high-quality granite. Trad climbing is the name of the game here and notable/large areas include Donner Summit, Lover's Leap, Woodford's Canyon, and Calaveras Dome, among countless other "smaller" areas that are just as good. Although not necessarily a bolt clipper's paradise, there are a few concentrations of sport climbing, including Big Chief, the Emeralds, and Bowman Lake. Further, most of the major (and minor) trad areas host at least a smattering of sport routes, if not a fairly substantial number (e.g., Donner Summit). Boulders are literally everywhere in Tahoe and to even try to grasp the volume of problems, pick up any of the 4 (!) bouldering guides currently available for the region...
Much of the climbing in the Lake Tahoe area is at higher elevations (6000-9000'), and is covered with snow for a substantial portion of the year. As such, the large majority of crags are best in late spring/summer/fall, although it can depend on how wet the winter is. Fairly reliable winter climbing spots include Sugarloaf, the south-facing side of Woodford's, Auburn Quarry, and a handful of other small, south-facing crags scattered about.
By Road
From the Bay Area, head up Highway 80 to Sacramento, where you will either head up into the hills either on 80, 50, or 89, depending on where you're going.
From Reno, head up Highway 80 to go to North Lake destinations, or down highway 395 , and then West on highway 89 into South Lake Tahoe.
By Air
The nearest city with commercial flights is Reno. For some Tahoe areas, Sacramento's airport might be a viable second option. Each one still requires a drive into the mountains.
By Rail
The first intercontinental railroad in the U.S. went over Donner Summit; one version of this line went through the Snowshed next to the climbing wall of the same name there. Amtrak still runs a train over the Sierra in this area, which runs through Truckee once a day or so. It's not cheap or fast compared to other modern travel to the Tahoe area, but is scenic (though it only goes by Donner Lake north and out of sight of Lake Tahoe).
Truckee, CA