I have a week to explore areas near San Francisco in the first week of December (driving there from Vegas via LA) can you suggest anything for an Australian? all I've heard is "Big Sur"
Big mountains are between Vegas and LA - perhaps go through Mammoth Lakes and Bishop on highway 395, you go skiing at Mammoth and see Mt Whitney, the highest point in the lower 48 states, while driving through Lone Pine.
Note all the roads crossing the Sierra Nevada mountains are closed south of the Lake Tahoe area after they get enough snow, usually in November.
From LA to San Francisco, take the 101 freeway through Santa Barbara, which has great beaches and hiking (writing this from there). Recommend the courthouse (Spanish Colonial architecture), the botanic garden and Butterfly Beach. The southern Los Padres National Forest stretches for 40 miles behind there in the hills, with some of the beautiful hiking and camping far off the tourist trail the parent comment refers to: http://santabarbarahikes.com/hikes/sanrafael/
Wine country for the next 200 miles north through Santa Ynez and SLO, then leave the freeway for highway 1 to go through Hearst Castle and Big Sur.
Note vast parts of all the above have recently been or currently are on fire, so consider calling the ranger station to check conditions before you go.
More specific recommendations depend on what you're into, but usually the weather is nice in early December, though getting down near freezing at night away from the immediate coast.
If there's rain in the forecast at the coast spend the week skiing powder at Mammoth.
After that, go to Santa Cruz. The Henry Cowell Redwoods State Park is the southernmost redwoods park on the coast. It's not quite as impressive as the Redwoods National Park much, much, much further north, but it's got the trees and the atmosphere. You're still south of San Francisco at this point. You can take Route 9 (a winding road) or Route 17 (a less-winding road) up to Silicon Valley from Santa Cruz.
Going south across the golden gate bridge, sometimes I just drive along the coast all the way south to half-moon bay, it's a great drive, and in December the Mavericks waves might be big. There is a black-sand beach along that drive, too.
This year, since the rainfall has been good, there will probably be some frozen waterfalls.
Muir Woods (which is under an hour away), Point Lobos...there's a lot of really beautiful stuff within a day trip of SF. I'd buy a tent, and plan to spend the night out for some of these, since most of the really good spots are at least a couple hours away.
That said, one could easily spend a week (month) on SF and Bay Area city exploration. There's a train that connects SF with the entirety of the rest of the bay area, so you don't even need a car to visit Mountain View (Computer History Museum is a must see!, though you'd want to catch a bus or Uber from the station to the museum, as it'd be a longish walk), Palo Alto (Stanford, Facebook, etc.), and several others along the CalTrain route.
Given how little time you have, I'd probably recommend you focus on minimizing travel time, and hit on stuff that's really close. That limits your "natural wonders" options, but there's a lot of really cool stuff made by people in recent history that's also worth seeing. SF is one of America's great cities.
Inland from Big Sur and equally south of SF, Pinnacles was recently made a national park. It can be fully explored in a couple days and, aside from the stunning volcanic scenery, is the first place the Califirnia Condor was reintroduced after very nearly going extinct. These days you can spot quite a few of them if you're willing to wake up early and watch the sunrise from the summit. The park attracts a crowd, and it's worth reserving a camp site early, but it's far less hectic than some of the better known parks.
Going east from SF, the Sierras has a number of wilderness areas that attract a fraction of the people you'd find in Yosemite (the valley is an absolute must-see, but it's a zoo outside of winter. The outdoors will require more gear in December, but the snow capped valley rim is one of the most beautiful places I've seen). If the snow is late in falling, I'm partial to Emigrant Wilderness - the same granite as Yosemite, none of the crowds. South of Yosemite, look into King's Canyon. Both should have snow in December, which is a good reminder to check seasonal road closures if you intend a scenic route across the Sierras. North of Yosemite, highways 120, 4, 88, and others typically close.
North of SF, Mendocino National Forest has an abundance of dirt roads accessing enormously underutilised public spaces. There's a drive-in campground just south of Snow Mountain (in the Snow Mtn wilderness) that's stunning and empty. Despite the name, it doesn't get much snow. Closer to the city, Sugarloaf above the Sonoma valley makes for a great low-key 1 or 2 day trip that can be worked into visiting a winery or two.
The Sonoma coast north of SF also has a lot of beautiful places. Check out Salt Point. A bit out of the way for Vegas, though.
Death Valley is mostly on the way to LV and in December will be cool enough to stand.
These are a few of my favorites that are varying degrees off the beaten path but all incredible natural places.