Early June in the Corpus area (and west of there) can be quite good, but mostly for roadhunting as antelope points out. They key is getting some rain. Less than an hour west of Corpus you can find milksnakes, kingsnakes, southwestern rats, bullsnakes, on the roads at night.
If it rains you could see other species as well.
There are indigosnakes in the general area, but to find them you need to be out in the morning hours and get lucky. Same is true for Mexican Hogs.
Western Diamondbacks and Checkered Garters are really common.
You can see some interesting herps at night on the roads on the northern end of North Padre island (before you get into the monument). That road can be kind of busy on weekend nights, however.
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Chris Harrison
San Antonio, Texas