Pretty sure US-34 is the longest East-to-West highway in the US. So, you could do that one. The thing is once you get west of the Mississippi River, beyond the Appalachians, you are driving in one big flat cornfield until you get to Denver. Once you reach the foothills of the Rockies, you have to make sure you’re driving in warm weather, because the snow up there shuts down every route in and out. Take 34 to I-25 South, then get on US-70, go over the mountains. Better views. After that, go through Utah via Zion National Park. Gorgeous. After that, you can keep west through Vegas, or detour south toward AZ and go to the Grand Canyon. Get Mexican food in SoCal. Skip Hollywood, it’s a dump. Get some Chinese food in NorCal. Go higher north into Cali if you like hiking in the woods. Washington is beautiful if you avoid rainy season. Montana has some insane sunsets/sunrises. Everything east of that is boring again until Chicago. Get seafood in New England, Del’s frozen lemonade in Rhode Island, pizza in NYC. Don’t bother with Texas, or any of the south. It’s hot, muggy, and boring.
If you wanna do it fast, you can do it (both ways) in a week. If you wanna do it right, you should do it in 2 weeks. This is a very basic rundown, and I’m sure other people have better advice.