Check the weather report. Very high chance of rain there this weekend, listed as 90% tonight as well. Since you didn't mention any mileages you want to or can do per day, can't make any real suggestions beyond what was already said. Personally I'd never go to Big Sur for just a night, too long a drive. Now going in Friday night and hiking in with lights for two nights total, that would be interesting.
Think about starting at China Camp and hiking in from there, staying up on the high levels, camp in one of the central camp places, can't remember the names, off of Pine Ridge trail, Bear Basin is one of them I think unless I got the name wrong, Divide might be another, I think that's right off the trail, but I could have it wrong. That's not a bad hike, about 3, maybe 4 hours depending on your speed. Somewhat reminiscent of the Sierras up there, it's cool. But the drive there is over a long dirt road, so that will add a lot to your time, probably a bad idea for an overnighter.
Big Sur ranger station to Barlow Flat on Pine Ridge is an easy hike, if you get to Barlow with 2 hours of daylight remaining, or an hour and decent headlamps, you can make it to Sykes, though most of the miles from Barlow to Sykes are uphill, but personally I'd rather stay at Barlow Flat, than deal with the overcrowded and over-impacted Sykes. If it's raining you'll see very few people though. Sykes is only between 10 and 12 miles, nobody knows for sure, all the signs differ in their mileages, but Barlow is a safe 6 to 7 miles I'd say.
I read that there might be some downed trees, but they might also have been cleared, they aren't a big deal, you just clamber carefully over them, it's kind of fun.
Watch out for Poison Oak and Ticks. Ticks are small, not big.
Also realize that there are very few flat spots in Big Sur's mountain areas, so you can't really just stop to camp unless you get to a campground, generally speaking. Consider that re hiking in the rain, ie, be prepared to actually hike to your destination all the way in the rain.