Contrary to popular belief, there is surf in Texas. We don't depend solely on hurricanes to provide waves. However, we live at the end of our own fetch. Most of the time the swells do not travel long enough to get classic but occasional offshore winds after a long steady onshore bring most of the quality surfing days. Strong onshore winds generated by the approach of an advancing cold front, generate swells starting a few hundred miles offshore. If this onshore flow lasts several days, the surf may build to "headhigh" or better. Timing is critical to catching quality surf in Texas. The weekend warrior seldom catches the best conditions, as the shift to offshore may change at midnight, leaving little left the next morning. It pays to be on it, just drop everything and go when the report calls it shoulder to head high and glassy.
When the "norther" hits, winds shift offshore. Depending on the strength of the front, you may catch nicely lined up surf with light offshores, or a howling (30 mph +) north wind that prevents even dropping in to the wave, and quickly blows the surf down to unrideable status.
Spring, Fall, and Winter bring the usually weekly cycle of fronts pushing surf. Sometimes the wind along the coast will drop as the front approaches, offering a chance for glassy, lined up conditions for those knowledgeable to the weather patterns. Spring usually offers the most consistant surf as frequent cool fronts pull moisture off the gulf, creating onshore wind and waves. Summer is the worst season for surf (the exception being a tropical system in the gulf).
Hurricanes do produce surf, but storm location and direction are critical. The best storms are the ones that make landfall a hundred miles or so north or east of your location. This will bring the offshore counter-clockwise wind around to clean up the swell. Storms that land west create onshore winds that make "victory at sea" conditions, poor for surfing. A storm hitting Louisiana will produce clean surf for the upper Texas coast, provided it came up from the middle of the gulf, slowly enough to generate a sufficient swell. South Texas surfers will get it from a storm hitting Galveston or Surfside.