Florida to Southern New Mexico

To avoid the worst parts of I-10 in Louisiana and the I-10 construction in Orange, TX, I'd use US-190 as some have suggested. You can jump over to 190 using LA-415 right after you cross the Mississippi on I-10. It's about 3.5 miles north to US-190. Stay on 190 to avoid the long, 2-lane (each way) Atchafalaya River bridge, Lafayette, Lake Charles (including the old, steep & narrow Calcasieu River bridge), the rough highway in Sulphur and the construction right when you cross into Texas in Orange. Take LA-12 at Ragley, LA. Continue on LA-12 on into Texas where it becomes TX-12 after you cross the state line and it rejoins I-10 near Vidor.

You probably want to loop around north of downtown Houston on I-610 and north of San Antonio on TX-1604, though there is no way to avoid the traffic completely in these two big cities.

Safe Driving!