Houston’s landmass is far and wide. From up near Tomball to down near Clearlake. However there are a lot of small incorporated cities with their own local governments surrounded on all sides by “Houston”.
Suburbs is an arbitrary distinction to me. What was once ‘outlying’ territory has since been swallowed up and ‘centered’ by further expansion and ‘new’ outlying suburbs, and so on, and so on.
Are the Heights suburbs? Montrose? Garden Oaks? Sharpstown? Spring-Branch?
Sorry, I do not know enough of the particulars about this & should not have answered. When friends ask for voting info, I direct them to the harrisvotes (for Harris County) website. It has a feature that will provide a customized - to their exact street address - sample ballot that will let them know what offices / issues they can vote on.