So this is a fairly vague question...The most common and most accessible coral reefs from the Galveston Bay Area is in a marine sanctuary called the Flower Garden Banks protected by NOAA. The entire sanctuary is made up of roughly 17 reefs but the 3 most common sites (and closest to us) are Stetson Bank and the East and West Flower Gardens. Stetson is about 80 to 90 miles from Surfside and the gardens are roughly 125 miles out. Here's a link to NOAA's website for it. Lots of good info.
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flowergarden.noaa.gov
Most folks use a charter service to dive it. I've only dove there once. It was over 15 years ago. The seas were rough and the water temp was still in the 60s. Because the water temp can get colder in this part of the Gulf, the coral and fish species that you can see will be very limited compared to what you might see in the rest of the Caribbean. At the time, for just a little bit more money you could go to Cozumel for a 4 night weekend where the diving was exponentially better...and the water was significantly warmer! So ever since diving the Flower Gardens, I've just resolved myself to go to Cozumel or Florida as opposed to doing a charter in the Gulf. My $0.02.