There is just one road to Padre Island National Seashore, and this extends only 5 miles south; the other 60 miles are both pathless and roadless, though accessible by walking or driving down the beach. The approach is via the 358 freeway through the center of Corpus Christi, across Oso Bay and the Encinal Peninsula then over the intercostal waterway and on to the island via the John F Kennedy Causeway, road P22.
PDF format maps of Padre Island National Seashore, from the National Park Service:
Detail map (276 kb)
Location map (88 kb)