Altitude in the southwest can be deceiving. The south rim of the Grand Canyon is at 7000' and the north rim is at 8000'. Bryce Canyon is around 8000-9000'.
I am sure you have seen pictures of people there but it does not appear to be so "high".
Your concern crossing the mountains should be about the grade and not the altitude. The I-10 grade is not noticable except there are are several grades that will get your attention for a short period of time. You will see a sign on I-10 notifying you are crossing the Contential Divide and are up around 4000' - but it comes at a complete surprise as the climb is so gradual.
There are other more pressing concerns when traveling out west - and wind is the one on my list that I watch. The wide expanse doesn't stop the winds and they can get pretty gusty. If in loose sand area sand storms are a real danger.
As for a grade to avoid - I would stay away from I-70 thru Colorado but it is one of the most beautiful drives in America.