I-70 is your most-challenging. Then, I-80 across Wyoming, to Salt Lake City. Easiest is I-40. The worst climb there, if you take I-25 south from Denver, is heading into Santa Fe.
Go to MapMyRun.com, and choose New Route. Then, in the settings to the right, choose Auto Route (for car, vs. run or bike ride). UNCHECK Avoid Highways.
Zoom way out, and just click along the highways. Don't need to click very often - I did about every-100 miles. Did each of the routes in about a minute, each. I just did the mountain area, as further east is not mountainous.
After the route is mapped, check "Elevation". This will show your elevation profile.
Good luck!
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