If you have 6 weeks to see the USA? My suggested itinerary would include 4 days in New York City, a travel day, 4 days in the capital, Washington DC, a travel day, 3 days in New Orleans, Louisiana, a travel day, 2 days to get to and see Carlsbad Caverns from Albuquerque in New Mexico, a travel day, 2 days in Tucson, Arizona, travel north and spend the next day at the Grand Canyon, a travel day and another full day in Las Vegas, Nevada, a travel day, 3 days in San Francisco, California, then 4 days to drive north to Calistoga and on to the Redwoods National Forest, 2 travel days to get to Wyoming and then 6 days to drive through the Grand Tetons National Park onto Yellowstone National Park and back, a travel day, 2 days in Chicago, a travel day, 3 days in Boston.
I see that comes to 46 rather than 42 days. If there is no leeway, you may want to jump from San Francisco to Wyoming; alternatively you could skip the Carlsbad Caverns in New Mexico. It’s an intense schedule but hopefully one with something for everyone. Don’t miss a boat trip on the bayou around New Orleans or the Sonoran Desert in Tucson. And you need not gamble to have fun in Las Vegas. Consider a mud bath in Calistoga, and visit the Old Faithful Geyser near there. If you can spare another day at the Grand Canyon (so you don’t collapse with exhaustion), hike down the Bright Angel Trail, camp half way back up and continue to the top the next day. If you prefer the outdoors to cities, you could skip Chicago and Boston to add Utah (flying into Salt Lake City) with stops at Bryce National Park and Zion National Park.
This is not a road trip but an itinerary assuming ample funds to fly between segments. It’s not quite the speed of light but it is jam-packed. As you asked, this is my suggestion. (If an option, the better way may be to visit one area at a time in 3-6 separate trips.) But if this is the one time visit… Wherever you go, remember to have fun!