I'd recommend to make a list of your top 5 priorities and then go with that. For a whole acre, you'll have to look pretty far out. Even living in Katy, there's nothing with a whole acre for several more miles out. It's Houston - you should be prepared to drive no matter what. As far as duplexes go, there aren't many here as far as I know. But you could find a property that has two houses on it, or put a second house or a trailer up. For using trailers, there are association restrictions in most places but it can be done in an area that doesn't have an association. What kind of commute with any other adults be willing to contend with?
You can check out http://www.har.com for available properties. There's a very good filter for criteria built into their site. Remember that the closer to downtown you go, generally the small the house, more expensive the property, you get. In the offset, the cultural sites are all centrally located. Museums, zoos, children's centers, are all mostly in the downtown and surrounding area.
For most residents of Houston that do not live inside the 610 loop, driving is understood.