Wait, are you driving a van or the Z?
Yosemite is a great detour and also has some killer roads if traffic doesn't suck.
If you do travel the easy I-80 route though Utah, then a high speed run on the salt flats would be a fun stop (in the Z that is). Other spots on my future list in UT are Zion and Bryce but those maybe too out of the way when going to SF.
You also mentioned Yellowstone which is great. If you do detour more North then you can swing by Mount Rushmore outside of Rapid City in South Dakota.
I would go this approximate route (the outdoor sites should be more dog friendly):
CT > Chicago, IL > Rapid City, SD > Yellowstone National Park, WY > Salt Lake City, UT (salt flats
) > Yosemite National Park, CA > San Fran