I hadn't really thought about this much before. I grew up in rural Texas outside Waco. Up and Down are for sure aligned with the map. Over isn't directional though. Out sort of is.
Over is something we used when the destination as specific to a person's location. Go over to the neighbor's in any direction. But also go over to my grandma's house. But if you didn't specify to her house, then it was out to East Texas for the weekend, not over. We'd go over to Mickey's place for a week, but out to Memphis. I'm sure this is not generalizable, but that's how it works for me.
In general, out is anything that's kind of a pain in the ass, and over is something you're a little happier about. And there's also the "in" to contrast with "out." When I was growing up we went in to town. And back out to the farm. And of all my strange Texas-isms, that's the one that gets me the most shit from New Yorkers. I live in Brooklyn, and so I say, I'm going in to town, when I go to Manhattan. And I'm going out to Brooklyn when I'm headed home. And it makes people seriously angry sometimes.
Some of the other strange things I grew up with, that are weird even to me:
"Cut the lights on." What? That doesn't even make sense? You can cut something off. You can't cut it on.
"I'm fixin' to . . ." mow the lawn, take out the trash, make dinner. Very often used when someone is nagging you about something you are not really about to do. You're just fixin' to do it.
"Let's get a colbear." It's a cold beer with the d dropped and a twang on the beer and all said as a single word with the accent on the co. It sounds really weird to this day.
We have really weird relationships with units of distance. We don't measure distance in units of length. We measure it in how long it takes us to drive there. I remember getting called out on this not long after I move to NYC. Some people I met wanted to know where the hell Waco is. And I figured if they live here and know any city in Texas, they will know Austin. So I gave position relative to Austin. "Oh about 2 hours up from Austin." 2 hours what? By subway? Jesus, that's terrible. I was like, "No, it's an easy drive. You just get on I35 and your there. Hour and a half if traffic is good and you speed a little." Finally had to break it down. It's a hundred miles.
Another related thing is that we don't think twice about driving distances that would have other people looking for a plane ticket. Fun fact: it's a longer drive from Texarkana to El Paso than it is from Dallas to Minneapolis. It's just a thing we grew up with. We like our cars, and we don't mind driving. I lived in Dallas for many years (and am about to move back soon). And I would often leave work an hour early or so, beat the traffic out of town, go have dinner with my parents and siblings (about a two hour drive), then drive home after dinner (another two hours), and not even think twice about it. Or if my brothers wanted to hang out and have some drinks, stay there, and just drive straight to work the next morning.
Tea is a weird thing here as well. I love iced tea, but not the way I grew up with it in Texas. I like what used to be hot tea, poured over ice until it's freezing cold. And unsweetened and without milk. But in Texas, there's a process for making sweet tea that's almost as intricate and cantankerous as making BBQ. You boil a quart of water, add 8-12 bags of cheap black teabags and stew those for about an hour. Take the bags out, and bring back to a boil. Then you supersaturate this bitter cauldron with sugar until it's basically a syrup. That concentrate is supposed to be diluted. But the problem is that whenever you're having someone over for an event that would warrant sweet tea, you're too busy making BBQ and doing last minute cleanup to dilute it properly, so you throw it all in an 8-quart pitcher, fill it up to the top with ice, and add some water. The restaurants don't do a much better job. It's basically like mainlining simple syrup with dark color and a bitter flavor. I hate it. But I'd be dead if I ever said that within state boarders.
And since I'm getting a little nostalgic, I'll wrap this up.
I've heard before that people who aren't from Texas think of our gas stations as grocery stores and our grocery stores as stadiums full of food. After 3 years in NYC, THIS IS SO TRUE! Nothing has been able to consistently frustrate me as much as trying to grocery shop here. It is so unreal what people have to deal with. And then when you go to 3 different hole-in-the-wall grocery stores (which may involve multiple subway rides, carrying your loot as you go) just to get the ingredients you need for one meal, the prices are so ridiculously high in the stores, that you really haven't saved that much money over just getting crappy takeout or delivery every night. Instead, you've wrecked your back lugging 80 lbs of groceries and wasted your weekend, and are pissed off anyway. I feel genuinely sorry for people who live here.