A bayside walk and a Port Isabel day
A weekday can make a short getaway easier to arrange, but it does not guarantee light traffic, an open museum or a quiet beach. This plan starts with the free Laguna Madre Nature Trail on the island, then groups two Port Isabel history stops on day two so you cross the causeway once.
Day one: a bayside walk
Visit the Nature Trail during permitted access hours and take time on the boardwalk. It looks over Laguna Madre habitat, not the Gulf surf. If you want the larger paid attraction next door, substitute the Birding & Nature Center and check its separate hours and admission. Leave the rest of the day for a beach entrance near your accommodation or an unhurried meal.
Day two: Port Isabel history
Start with the Port Isabel Lighthouse. The Texas Historical Commission explains that tower access is weather-dependent and has climb rules, so the visitor center and grounds are useful alternatives when the stairs do not work for someone in your group. Add the Historical Museum only after confirming its current weekday hours.
Look at bridge traffic before leaving and again before returning. Saving the three suggestions does not confirm that they will all be open on the same weekday.