Reno resident here. It will be nearly impossible to get something anywhere on Tahoe, regardless of side. Everything is booked up 6 month in advance. That being said, my daughter got a cancellation for last weekend a week before at Bliss on the west side, so if you are diligent you might find something. There are fewer campgrounds on the east/ nevada side. Check mt rose (Forest Service). Or Davis creek (Washoe County Park) or Washoe lake (NV state park). Davis creek and Washoe lake are both nevada state are first-come. You can also make reservations at Washoe Lake. You could snag something there. To my knowledge, none of nv side campgrounds will have a lake view, but they are close, within 20 minutes of the Lake. We just camped with several teardrops at mt rose several weeks ago. It is a forest service campground, small but really nice and very close to Incline and South Shore of the lake. Plus at 10k feet it is 20 degrees cooler than the 98 we are having right now. While it was booked, there were several last minute cancellations for a couple of trailers to get in and snag a site for one night or two nights. It won’t be posted on the website, so you would have to chance it.
https://www.recreation.gov/camping/campgrounds/232186If coming through during the week you should be able to get a site at either Washoe Lake (desert camping) or Davis creek (more protected/ trees). Both have showers, and Washoe has some hookups if you need to charge your battery. FYI, Nevada beach is nice,a s it is one of just a few on the lake itself, but it is also at Zephyr cove just out of South Lake Tahoe\Stateline and an urban area. Traffic this time of year, well any time of year, is historically awful around south lake. Avoid if possible. Two lanes highway, competing with day trippers parking on the side of the road, coming and going most of the ring around the lake. I would not take my teardrop to zephyr cove on a weekend, also not through Stateline or Tahoma/Tahoe City if you can avoid it. Been there, done that. Coming through Carson, Davis Creek and Washoe Lake will be very close, both off 395/580 south.
http://parks.nv.gov/parks/washoe-lake https://www.washoecounty.gov/parks/specialty_facilities/davis_creek_campground.php That being said,Lake Tahoe is unbelievably beautiful, and don't come all this way without seeing it. If you have time, I highly recommend the Lake Tahoe Shakespeare festival at Incline. The theater is outdoors on the lake and the venue is incredible. The alternate nights of a Shakespeare play and another. This year, Mamma Mia, which we saw and loved. Its a short drive from Mt rose campground and only 30 minutes from Davis creek or Washoe Lake.
https://laketahoeshakespeare.com/When are you coming? If coming now through Labor Day it will be tougher due to burning man
https://burningman.org/ attendees coming then going, esp. now to aug 30 then sept 4-6. But we have always been able to snag a spot over Labor Day above Donner lake (very close to Tahoe) on 89 above Truckee. There are 3-4 forest service campgrounds there between Truckee and Sierraville. Cottonwood creek is the best of them. And keep in mind that 80% of Nevada is public lands (BLM). That means unless posted as private or no camping, you can always just pull over, pull off, or go off and explore and find a spot to camp.