Id also stop on the way west. We drove through but didnt spend much time at BL. There is a boondocking spot on the east side of the highway before entering the park. Wasta has an overnight spot with electricity and dump station for $10 along with a military museum. We also also stayed at Legion lake. I dont remember the site number but it was on the left in back by the loop. Two or three sites back there have some shade. The deer would wander in but so do the buffalo so pay attention when exiting your rig. There was firewood behind the loop and hiking trails out back.
Sylvan lake is beautiful and has a swimming area and island rock. Between Legion lake and the wildlife loop there is a side detour up to the tower with a view for miles. Also try to make it to Crazy Horse. Its just me but when I go back it wont be for the BL, it will be in the Black Hills.
We were riding our bicycles around the dead little town of Wasta when I started chewing the fat with a local sitting on his porch. I asked about all the closed up motels etc and he said do you see that crumbling road right over there, it's the old Black and Yellow highway. It was the route from Chicago to the BH and Yellowstone before the freeway went in. The guy said he used to ride his Harley to Strugis every year and retired from a big place in Mich and figured why not move out there so he found that little pole barn house for $17K and sits out on his porch.
I went 79 to 36 to 16A to Legion lake and didnt tow anywhere in there. I did help guide a lady through one of the tunnels and take pictures for her but it was a crazy tight fit. :) I gotta get back out to Legion Lake, it's a beautiful area. To me it just had a great feeling.