Worldwinds is a business which rents and sells windsurfing equipment. They also happen to teach excellent windsurfing classes.
Worldwinds is located inside the Padre Island National Seashore, a national park. This means that you will need to pay admission to this park and also pay for parking on Bird Island. Admission is good for seven days, but parking is only good for one. The fees can be found here. You may wish to get the annual passes for both -- I have them and they only cost twice the normal costs.
To get directions to Worldwinds, you can use Bird Island Basin Rd., Corpus Christi, TX as its address. The business is located at the west end of that road, on the beach.
Update: It is important to note that there isn't any running water in Bird Island Basin. There are public restrooms near Worldwinds, but they have hand-sanitizer dispensers instead of sinks. This is one reason why it is critical to bring lots of bottled water when you visit.