The 60 southern miles of 'North' Padre Island that lie outside Corpus Christi city limits are all a protected part of the Padre Island National Seashore. Endangered Kemp Ridley sea turtles nest in the park and are closely protected. If you're visiting in late summer, you might be able to take part in a turtle release.
The constant wind not only creates and moves dunes, it also attracts kite- and windsurfers to the inland-side Bird Island Basin area. There you can rent kayaks, windsurfing gear and stand-up paddleboards from Worldwinds.
Four-wheel drive is necessary to see the extent of the park, but if you hike even a short distance from the visitor center you'll be free of the crowds. Camping is available at the semi-developed Malaquite and Bird Island Basin campgrounds ($8), or go primitive – beach camping elsewhere is free with a permit.