Are there any beginner friendly off road spots around Houston?

Hey y’all! I’m trying to plan out a weekend off-road/camping trip thing for my S/O and I am absolutely clueless when it comes to these things. I’m trying to schedule this in January (temperatures permitting). We have a more than capable vehicle and would be willing to travel as far north as Austin-ish and as south as Matagorda. Looking to spend under $400 total for everything (gas, consumables, fees/spot rentals, etc) but it’s not a super big deal. Any help is appreciated! Can cross post if someone has a subreddit to recommend. Thanks!