Camp. Hike. Lake. Dirt Road. Go to here.
At first we couldn't find this place because Google Maps will take you to the entrance of Sitting Bull Campground down the road. Follow the directions on reserveamerica.com or just head west from Sitting Bull Campground about 4 miles and turn on West Tensleep Lake Road.
It's a dirt/rock road and you'll be on it for 7 miles. Along the route is a half dozen other campgrounds. Each time you approach one you'll get excited thinking it's yours but it isn't. Don't worry. West Tensleep Lake Campground is better than those campgrounds.
Finally, you'll arrive at the last campground on the road which is also the trailhead. It is only 10 spots that are tent only. Half along the lake-side and half road-side. If you can take a lakeside spot (you can reserve these). The road side ones aren't bad but they are more exposed and a bit less wooded. Each site has a parking spot, picnic table and fire-pit with grill. Camp is at 9000+ elevation so when you search for weather reports they will not be accurate. The nearest town, Tensleep, is about 4000 ft lower in elevation so the weather can be dramatically different.
There are vault toilets which are probably the cleanest toilets I/we have ever seen in a campground. They were clean when we got there, cleaned while we were there and still clean when we left. There is a by the book Park Ranger who will sell you wood (if you arrive at a weird hour or don't want to wait stop by the second campsite on the road and you can buy wood there). He will also give you a speech about bears and a massive hefty bag for trash which seemed like major overkill, not to mention a lot of wasted plastic.
The lake is shallow (snow dependent?) but beautiful and teeming with beavers, fish and usually at least one canoe. It is deceptively large, and you can see Big Horn National Forest surrounding it and mountain peaks in the distance. There is a trailhead where you need to fill out some paperwork when you leave on a hike and then trails heading off for miles in a few different directions. We followed the lake to the northern end and then followed the path along creek/river into the woods. It was easy hiking, but really beautiful and worth the effort to get down that long road at the beginning.
On a 5625 mile road trip through forests and parks this campsite was a highlight. Stop in Tensleep on the way out of town. It is worth a visit.