No Colorado city borders Texas—the states are separated by New Mexico and Oklahoma. The closest major Colorado city to Texas is Denver, approximately 700 miles (1,125 km) from the Texas panhandle (e.g., Amarillo) via I-25 S to US-87 S/I-27 S.
Driving time: ~10.5–11 hours. For southern Texas destinations (e.g., El Paso), the distance from Denver exceeds 800 miles.
If you're in southern Colorado (e.g., Trinidad, Pueblo), the drive to the Texas border is shorter (~150–200 miles), but these are smaller towns, not major cities.