Houston is huge, so first thing is to rent a car from the airport. You will need a car, more cost effective than relying on taxis, uber, etc.
The Galleria is the place to be. Crime is everywhere, but for out of state visitors, Galleria is place that I would stay with my family. It is pretty central to all the subdivisions (Woodlands, Pearland, Sugarland, etc) you want to visit via the 610 Loop and I-69 (old Hwy 59). The area surrounding the Galleria (Montrose, Richmond, Westheimer) has that New York Greenwich Village feel to it.
Houston Zoo, Hermann Park, Texas Medical Center, Houston Museum of Fine Arts, etc are all centrally located near the Galleria. Try to fly into Houston Hobby Airport if you can cuz it is closer to Galleria. But if end of staying in Woodlands, Tomball, Spring area (all in North Houston) then closet airport is Bush Intercontinental.
Cost of living wise, Houston is lower than DFW (I believe) and know it is lower than COA in Washington state (visited there before, near Bellingham, WA). Ex. Have many Californians selling their homes and coming to Houston and buying bigger/more amenities single family homes in Pearland, Sugarland for half the price of their tiny homes in Cali.