I do not recommend US 59 south from Houston. This is due to the "white knuckle" syndrome of narrow lanes with construction and heavy traffic for several miles. We went from Beaumont to Port Aransas that way last August. I came back via Texas state highway 35 to state highway (freeway) 288 and had much less stress, though it took a little longer. I would recommend looping around downtown Houston via Beltway 8/Sam Houston Parkway (tolls) or I-610 loop. You can also come straight through downtown on 59 and take 288 from there (shorter but more traffic). Just a suggestion. Safe travels to you!