SF -> Philly Road Trip Suggestions?

I’ve never gotten to do a cross country road trip but my girlfriend and I will be doing it because I’ll be going to Drexel and she’ll be going to UPenn GSD.

BTW, I put SF because not everybody will know where Oakland is, but that’s where we live.

Due to the way our summer and fall classes line up, we will either be driving across from July 28-Aug 6 or Aug 19-28. She wants to see the Grand Canyon/drive through the southwest a bit (she likes cool deserts), and I was thinking I want to drive through Montana/the Dakotas because of the high speed limits and supposedly beautiful scenery. Both of us agreed we aren’t very interested in driving through the deep south, and since we are going to Philly anyways there isn’t really any need to. I was thinking maybe drive from OAK-Flagstaff, see the canyon, drive up to Montana, and then drive over from there. Any thoughts/ suggestions? I’ve traveled a lot out of the country but barely at all within the country. I’ve driven around New England, Chicago, Las Vegas, Denver, and Florida, but not really anywhere besides that.

In addition, a general question: Is it better to try to drive nonstop for 12-16 hours and then spend more time out of the car exploring? Or to just drive for 8-10 hours a day and spend a few hours stopping during the travels to explore?

I have friends in Polebridge and Bozeman (MT) as well that I’d like to visit if I can. So a preliminary idea would be something like:
Day 1: Oak->Flagstaff (we could drive through Vegas on the way)
11.5 hours of driving

Day 2: Half day grand canyon, then Grand Canyon->Salt Lake City, UT
8 hrs of driving

Day 3: Salt Lake City->Polebridge, MT
10.5 hours of driving

Day 4: Hang out in Polebridge

Day 5: Polebridge->Bozeman
6.5 hours of driving, then hang out the rest of the day in Bozeman, and sleep at my friends place.

Day 6: Bozeman->Fargo, North Dakota
10.5 hours of driving

Day 7: Fargo, ND->Minneapolis
Only 3.5 hours, so we would have time to relax, drive to Minneapolis, sightsee, maybe there’s some cool stuff going on there. I was always a huge fan of the minneapolis hip hop scene too.

Day 8: Minneapolis->Detroit MI
10.5 hours of driving, we could stop in Chicago for lunch or dinner.

Day 9: Detroit ->Philly
9 hours of driving.