Actually, Houston saw their first 700+ footer in 1971, but the bulk did come in the 80s. The first 700 footer in Houston was the One Shell Plaza at 714 feet and 50 floors. It was the tallest building in Texas from 1971 to 1980.
One Shell Plaza
Dallas saw its first 700+ footer in 1974 with the Renaissance Tower at 710 feet and 56 floors. That building was Dallas' tallest from 1974 to 1985. In 1987 it was added onto to become their 2nd tallest and it also became the first 800 to 899 foot building in Texas after the additional height.
Renaissance Tower