I would reccomend the northern route one way and the southern the other.
The northern route is the one I have done and it is I-80. Goes past Great Lakes, then once across the Mississippi follows the route of the Oregon Trail. Lots of incredible history to see, old forts, Chimney Rock, Salt Lake City. In some spots you can still see the wheel ruts left over 100 years ago. Just amazing. You go through Salt Lake City and then could go down towards Las Vegas and LA. Went through South Dakota, Montana, Wyoming, etc. The Wild wild west.
I have not done the southern route but it can go past the Grand Canyon and then through the southern states and cut back up.
Have fun and with an 11 year old there is so much to be learned and studied in such a hands on fun way.
And that before you even get to the "fun" stuff!
Jennifer