Thanks for all of the thoughtful responses everyone! We decided to skip the RV and are instead going to rent a big SUV and are going to make the trip over 7 days and stay at AirBnBs where our pup can hang out while we explore. We are early risers, so we'll likely be on the road every day at 6:30/7A so we can get where we are going with some daylight left to explore.
Here's the plan we came up with:
Day 1: 9 hours (a long day) to Indianapolis. This is really purely a travel day, but we will try and find some places to check out in Indy.
Day 2: 4 hours to St Louis, MO. Easy driving day and plenty of time to go see the Arch and maybe check out the zoo.
Day 3: 6 hours to Salina, KS. Mid-range day, but we can make it by mid afternoon. We'll eat way too much BBQ and find something fun to check out.
Day 4: 6 hours to Denver, CO. Mostly site seeing planned and enjoy the views.
Day 5: 7 hours to Richfield, UT. Again mostly a site seeing day, but we'll get some hikes in that are right near the cabin we are renting.
Day 6: 8.5 hours (the last long day) to Reno, NV. People watching and exploring a cool city.
Day 7: 4 hours to San Francisco. We have arrived!
Going to try and find some cool places to stop mid-way each day which will add an hour or so to the travel times, I figure.
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That's a clever idea! If we were going somewhere we had more of a support system to land in, I think this would work. The kids and I would totally be fine without mom, but she wouldn't be comfortable getting there solo.