Answer:
1) Take I-10 EAST through Arizona to I-25 NORTH to ALBUQUERQUE at EXIT 144 in Las Cruces in New Mexico.
2) Take I-25 NORTH to I-40 EAST to SANTA ROSA at EXIT 226A.
3) Take I-40 EAST through New Mexico, Texas, Oklahoma, Arkansas and Tennessee to RALEIGH, NC. On this route you will bypass only 2 cities: Nashville
via I-440 (EXIT 206) and Knoxville via I-640 (EXIT 385), both in Tennessee.