I get this question a lot. Often, people from out of town visit the Medical Center while a family member or friend is receiving medical treatment. Although they often spend the majority of their time at the medical center, they may have some time to experience the area or go out for a meal.
Houston weather can vary significantly so that will impact which options to consider.
The list is focused on the Museum District, Hermann Park and Rice University Areas.
Museum of Fine Arts Houston (MFAH) (https://www.mfah.org/). Visit the top of the Glassel School of Art (https://www.mfah.org/visit/glassell-school) for excellent views of downtown, Hermann Park and Rice University.
Houston Museum of Natural Science (https://www.hmns.org/)
Rice Village – cafes, pubs, restaurants, shopping (https://rice-village.com)
Armadillo Palace – a restaurant that is uniquely Houston.
The Menil Museum (https://www.menil.org/)
Rothko Chapel (https://www.rothkochapel.org/)
Hermann Park (https://www.hermannpark.org/points-of-interest/)
Hermann Park Japanese Gardens (https://www.hermannpark.org/poi/24/) As a reader, this is one of my favorite spots. Take a book with you.
The Houston Zoo (https://www.houstonzoo.org/)
Rice University Campus (https://www.rice.edu/campus-maps) Nice place for a walk under the canopy of trees. There is also a walking/jogging path around the campus.