A pet outing with a published policy
Sea Turtle, Inc. is the scheduled stop because its current visitor page explicitly welcomes well-behaved pets on leashes and asks owners to keep them close and clean up after them. Check that page again before visiting, bring what your animal needs and be ready to leave if the setting is stressful. Parts of the visit are outdoors, so the day's heat matters.
Add a city-beach walk only if it suits your pet
The City of South Padre Island's beach guidance tells visitors to keep pets leashed and clean up after them. Compare city beach accesses and choose an actual walkover near your accommodation instead of assuming every park has the same pet policy. An older City pet-beach tip sheet also points out the practical basics: fresh water, shade and protecting paws from hot sand and pavement.
For Andy Bowie or Isla Blanca, ask Cameron County Parks about the current day-use pet rules before making plans. City beach rules do not establish permission at county parks.
Keep your animal's vaccination record and emergency contact handy, and do not leave a pet in a parked vehicle. Saving this idea adds only Sea Turtle, Inc.; the beach walk remains your choice after checking the day's rules and conditions.