Don't know about the South end of the island, I'm up near Corpus Christi. There are some good roads North of Rockport in and around the Aransas Wildlife Refuge - winter home of the Whooping Cranes. You might look farther West and Northwest of you around the Rio Grande Valley towards Falcon Lake.
I was just visiting; threw the KLR in the back of the pickup so I'd have something to ride while my wife was beachcombing. Really enjoyed the trip, even though it was unseasonably cool (still way better than at home.) We'll be back.
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