Houston and Portland are about 1,834 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 15 hr 47 min of driving on the Houston side and 23 hr 12 min on the Portland side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Albuquerque still makes a fair, central place for Houston and Portland to converge, splitting the travel instead of asking one side to cross the country.
If Albuquerque doesn't have what you're after, Denver and Salt Lake City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Portland.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.