From Indiana to Yellowstone

By all means, go around. Traffic doesn't move very fast in YNP. Lots of things to see. If you don't already have a National Parks Pass get one, preferably before you leave home. It gets you through the entrance(s) faster each day. I always stay at Yellowstone Grizzly RV park when I visit. They have FHUs, and free coffee every morning. And you're two blocks from the west gate. West Yellowstone also has more than one grocery store, so prices are reasonable. Or at least more reasonable than in the park. One other thing. Each morning, a herd of Bison cross the west entrance road, headed for a big valley to graze. Do not try to drive through them. Their skulls can put a pretty big dent in your vehicle and they won't feel a thing. If you don't plan on taking a camera, change your plan. Photo opportunities are everywhere.
You didn't say how long you intend to stay, but if you have the time, visit Grand Teton NP, just south of Yellowstone. The beauty of GTNP will take your breath away.
And on your way home, you can start planning your next visit. :)