Glad to see some questions near me. I went to that area last year, but I didn't have the Tesla with me. Yeah, going straight across highway 20 from Boise to Arco is possibly going to be too long probably with bikes hurting your aerodynamics. But I think charging up in Twin Falls and then heading up highway 26 should be totally easy (like just over 100 rated miles, plus some extra for the bad aerodynamics).
We stayed at the KOA campground in Arco, which is a really great place, and I would totally recommend it. We were tent camping, and they even had TT-30 outlets right next to our site, which we could have used. We also saw a lot of really big RV's, so I think they have 14-50 outlets at those other spots too. Call and make sure of that.
The entrance to the Craters of the Moon area is only about 20 miles back west of Arco, so I would still recommend staying at the KOA in Arco, where you can actually have a decent restaurant there in town for dinner and breakfast.
We did this trip on a weekend and saw a few really good things. On Saturday morning, we saw Experimental Breeder Reactor 1, which was the first nuclear reactor in the world to generate electricity. They do excellent guided tours seven days a week, but it's only open from Memorial Day to Labor Day. Then, we did the Philo Farnsworth TV and Pioneer history museum in Rigby. It's dinky and quirky and kind of interesting and is only $2.
Then on Sunday, we started back toward Boise, so we went to Craters of the Moon and got to crawl around in some of the underground caves, which was really cool (literally). Then, we went to the Shoshone Ice Caves, which are on highway 75 north of Twin Falls. Since you would probably be coming up from Twin Falls on your way out to Arco and Idaho Falls, you could see that on your way out there. There's a terribly cheesy gift shop you have to wait in before the tour, but the cave is really interesting.