Looking for schools 2024/2025

Wife and I are moving to Houston next summer…coming from Cleveland Ohio (wife’s wrapping up a mfm fellowship and starting a fetal surgery fellowship). We would like to live within a decent distance of the med center for obvious reasons, definitely renting to start out and get our feet under us, figure out where we want to eventually settle in the city. Our son will be in second grade, currently attends a magnet school for gifted students here. Ideally we would love to get him enrolled in a non-zoned elementary school so we can be more lenient with looking for a place to live. I work from home so can drop off anywhere. What’s our best options in the inner loop for cheap private or public/magnet/gifted schools that you can attend while not living in the zoned district? Thanks for all answers.