It would be helpful if you could tell us more about your situation. What time of year? What are your interests? How long do you have, and will you be spending more time sight-seeing than driving or vice versa? Going on the cheap, or luxury, or somewhere in between? And so on.
Time of year matters a great deal. The most direct route from the Twin Cities to the Bay (basically following I-80) is great for summer travel and lousy in the winter. The Route 66 option that others have recommended is painfully hot in the summer, but excellent in spring and fall. And so on.
That said, and assuming a summer trip, the one must-see along your (relatively) direct route is Yellowstone National Park. (BTW, it's none too soon to start planning accommodations for Yellowstone for next summer; things book up incredibly far in advance.) My recommendation would be to use Yellowstone as a "pivot point" on your trip and plan everything else around it. Some worthwhile things that combine well with Yellowstone and your starting and ending points are:
* Badlands and Black Hills -- in my opinion Mount Rushmore is overrated and more of a drive-through than a destination, but there are plenty of other things in the Black Hills that are interesting, notably wildlife
* Devils Tower National Monument -- rather far out in the boonies, but directly between the Black Hills and Yellowstone so it's on your way
* Thermopolis, Wyoming -- small town with a honking big hot spring that you can bathe in (at a developed bathhouse); the drive between Devils Tower and here is spectacular
* Grand Teton National Park -- some of the prettiest mountains in the Rockies, and a natural way onward from Yellowstone
* Salt Lake City -- not really much point in going out of your way to see big cities (San Fran being more interesting than most along the way), but Salt Lake is on the way, and relatively interesting
All of this presumes that you've never been through this part of the country before, and therefore don't mind doing some of the more "usual" things. To get off the beaten path, you'd want to do some other things, but it really isn't necessary for a first-time visitor. Please give us more info and we can give you more help.
Bill-on-the-Hill
Tell us more
It would be helpful if you could tell us more about your situation. What time of year? What are your interests? How long do you have, and will you be spending more time sight-seeing than driving or vice versa? Going on the cheap, or luxury, or somewhere in between? And so on.
Time of year matters a great deal. The most direct route from the Twin Cities to the Bay (basically following I-80) is great for summer travel and lousy in the winter. The Route 66 option that others have recommended is painfully hot in the summer, but excellent in spring and fall. And so on.
That said, and assuming a summer trip, the one must-see along your (relatively) direct route is Yellowstone National Park. (BTW, it's none too soon to start planning accommodations for Yellowstone for next summer; things book up incredibly far in advance.) My recommendation would be to use Yellowstone as a "pivot point" on your trip and plan everything else around it. Some worthwhile things that combine well with Yellowstone and your starting and ending points are:
* Badlands and Black Hills -- in my opinion Mount Rushmore is overrated and more of a drive-through than a destination, but there are plenty of other things in the Black Hills that are interesting, notably wildlife
* Wind Cave National Park and Jewel Cave National Monument -- Wind has camping and more stuff above ground, Jewel is the more interesting to tour
* Devils Tower National Monument -- rather far out in the boonies, but directly between the Black Hills and Yellowstone so it's on your way
* Thermopolis, Wyoming -- small town with a honking big hot spring that you can bathe in (at a developed bathhouse); the drive between Devils Tower and here is spectacular
* Grand Teton National Park -- some of the prettiest mountains in the Rockies, and a natural way onward from Yellowstone
* Salt Lake City -- not really much point in going out of your way to see big cities (San Fran being more interesting than most along the way), but Salt Lake is on the way, and relatively interesting
All of this presumes that you've never been through this part of the country before, and therefore don't mind doing some of the more "usual" things. To get off the beaten path, you'd want to do some other things, but it really isn't necessary for a first-time visitor. Please give us more info and we can give you more help.