In all honesty, genshin impact is a pretty reasonable facsimile of that sort of game. It's really grown into its own, and it's really fun and absolutely massive

That said, I'd only advise it if you are 100% confident you won't engage in any of the gacha systems -- you can play and enjoy the game with the free characters the game gives you, but once you start engaging with the gacha that can be a really dangerous slippery slope. If that's something that you could fall prey to, I wouldn't recommend it. But if you think you can play it without investing any money (or, really, more money than you can afford, I don't know your financial situation) it's actually a really great time, and the story's only gotten better as it's gone on. There's definitely some stipulations with it, but it's worth experiencing if you feel like those are acceptable

Dark souls 1. No other game made exploring the world so exciting. I was checking every single nook and cranny because the game isn't afraid to give you good gear if you look. The combat can be frustrating but the further you get the easier the game gets. Also definitely follow a build guide if it's your first ds game.

Have you looked at "immortals: Fenix rising"?

It has borrowed many elements from botw but with a lot of the "Ubisoft open world formula" on top. I really enjoyed it. The combat is deeper than botw in the traditional sense but I found it responsive and easy to learn. The "shrine" equivalents also had some interesting and unique challenges too.

Perhaps you may or may not enjoy ~~Space Asshole~~ Red Faction: Guerilla. It's a 2009 game that got a solid enough PC port that may run on weaker systems. There's a remastered version but if you're aiming for low-spec the original might be a better bet.

Anyway, it's an open world set on Mars and you go around wreaking havoc and blowing up buildings with ahead-of-its-time physics/destruction mechanics. The combat is more like a shooter and you play with lots of explosives. It's not a huge map by standards today but is a big enough playground to keep one occupied.

similar open world games with good combat systems,

This might be a tall order. Most of the "open world" games I've found either fall down in the open world department (lots of restricted areas or nothing varied/interesting enough to make exploring fun) or fall down in the combat department (awkward, unresponsive, or annoying in some other way). Some high-profile games even manage to suffer from both these problems despite being great in other ways (I'm looking at you, Geralt).

I hoped for quite a while that the next Elder Scrolls game would keep the good parts of Skyrim (beautiful environments full of unique things to discover) and overhaul the combat into something good, but recent showings from Bethesda make me less than optimistic.

Some people praise the Dark Souls series (including Elden Ring) for both openness and combat. However, if you loved Breath of the Wild, I wonder if the Souls style would be a bit too combat-focused for your taste, leaving the world feeling cold and empty. I haven't played them enough to have a strong opinion about this; perhaps someone else can chime in.

I look forward to the suggestions you get in this thread.

Edit:

I just remembered Subnautica! I recommend this game, but there's caveat in the context of your question: The way it avoids bad combat is to give the player reason to avoid combat as much as possible.

Maybe Valheim?

Assassin's Creed 1 and 2. I've also heard good things about Morrowind but haven't played it.

I see a lot of MMOs being recommended, but I find them to be either shallow in combat or predatory unless you are seeking MMO specific things, so I'm going to point at single player/coop stuff.

Bethesda has a large selection of open world games, but I pretty much assume people have played all of them (Elder Scrolls / Fallout games).

If you are okay with going outside of Fantasy, the Far Cry series has some impressive technology in their older titles. Far Cry 2 is a personal favorite, your PC might be able to handle it.

Borderlands series.

The original Dragons Dogma: Dark Arisen holds up. This is probably my best recommendation based on your asks.

Lego Star Wars or the Lego Marvel game.

Fable 1, 2, 3

The Middle Earth Shadow of Mordor / Shadow of War Games were pretty incredible but might be too high-end.

The first Red Dead Redemption might run for you.

Early Dark souls games might run. Maybe 1 or 2.

From here, I would start listing old Star Wars Jedi Knight series games.

I could probably go on, but this is most of the good stuff off the top of my head.

I forgot to add Mass Effect. Great for sci-fi, great leveling, and combat.

I just finished playing Horizon: Zero Dawn for the second time and it was way more engaging than I remember it being back in 2017. Apparently a lot of reviews ragged on it for “not being Breath of the Wild” which is a lame thing to complain about, even if the game came out at the same time, and they share a lot of thematic elements (like heavily focusing on archery, fighting ancient machines, exploring a beautiful world, etc.).

But it’s a very different game, very narrative heavy, very beautiful, and very well-optimized on PC. The combat is very focused and fun in a good way.

Not precisely open world but has the same feeling of exploration, discovery and unlocking, Supraland. Harder puzzles, unlock things that make combat easier. Combat is pretty similar to botw.

Baldur's Gate 3 isn't exactly open world in the strictest sense, but the maps are so massive that you can get the same sense of wonder and exploration as something like Skyrim or BoTW.

What are the exact specs (CPU, GPU, RAM, SSD yes or no) of your PCs? "Kinda weak" kinda covers an enormous and very subjective spectrum.

Others have mentioned Elder Scrolls, but nobody recommended Daggerfall yet, so it's one of my picks. Yes, the 1996 game, which you can play on Unity for a much, much better experience overall. Since the game is free, you don't need to pay a thing. Combat won't feel good, tho.

If you enjoy space games, X3 Albion Prelude might be a good option. It's "open world" in that you can go anywhere right from the start, but the main gist of the game is to get rich so you can get the capital ships. Ship to ship combat is fine, each ship class has strengths and weaknesses. It has a learning curve and can feel needlessly convoluted at times

Kingdoms of Amalur isn't really open world, but its combat is awesome. Get the original, non-remastered version, and it should run on your stronger PC, hopefully.

I don't know how weak you're talking, but Horizon Zero Dawn has that same engaging, high skill ceiling combat that BOTW/TOTK does. The minimum specs don't look too bad, and the game is quite well optimised. Forbidden West is probably a no-go, though, and it's a much better game which serves as a true direct sequel. They're great if you like story, too.

The Zero Dawn Steam page.

As well as Forbidden West.

Everyone else has already made great suggestions too. This was the only different suggestion I could make.

Noita is on sale!

It's not Zelda like, but if you like factory games, Satisfactory is as close to open world as a factory game gets. You land on a planet and have to build a factory to launch things into space for corporate overlords. It's first person, lots of climbing and building. There's a tiny bit of combat, not the focus tho.

You might really enjoy DayZ. The public servers are pretty brutal, but if you find a comfortable RP server you can settle in and really enjoy exploring the landscape. Once you're used to the mechanics it's so smooth.

Stereo headphones or even like monitors make hunting a lot of fun, listening to distant sounds trying to find a deer or boar is a lot of fun. And once you're used to dealing with zombies and the sthough.l mechanics, crafting and all that, it really opens up.

Plus the ability to expand it with modding is pretty extensive. We've got some neat stuff on our own server (though not much pop atm), and I've seen others that do some next level stuff like player vampires and werewolves and stuff.

Even just the vanilla game is absolutely gorgeous though. If you like exploring, scavenging, and crafting, especially with friends, it's kind of perfect.

Conan Exiles has a somewhat similar vibe but a bit clunkier and in a low fantasy setting. It's also got a lot of D&D roleplay servers.

My somewhat controversial suggestion is outward. Low graphical intensity PC game, very open world, and some incredibly unique and polarizing design choices. If your favorite part of breath of the wild was world exploration and korok finding, you may love it! If you like quality of life features though, maybe not.

Things like, you have a world map but no "you are here" marker so need to place yourself with landmarks. You need to drop your backpack to fight effectively and remember where you dropped it, the magic system is based on insomnia with the longer since you slept the more mana you have until you push it too far and just collapse. Really really weird game that I still think about all the time years later.

Warframe might fit what you're looking for.

It has an overarching story and story missions, it's combat oriented, it has one of the least-predatory F2P models I can think of, and it has both open world zones and "interior" missions.

Best of all, it runs on potatoes. Might be worth looking into.

Another option is maybe Monster Hunter Rise, but I've only played a demo, and you have to consider Capcom's aggressive anti-cheat back porting.

Last one you might not have considered is Halo Infinite. I played the entire campaign with a Ryzen 5600G on medium settings and got ≈45-55fps. It's very well optimized and should run fine on weaker hardware.

Piggybacking on my genshin suggestion, another suggestion would be Guild Wars 2? It's world is more open than most MMOs and since it's over a decade old there's a ton of content there. There's a lot as a free2play player, but you can buy expansions if you want even more to explore, and I genuinely think gw2's exploration is best-in-class. It's also benefitted by being an old game in terms of old computers being able to run it, you'd probably have to play on low graphics but it'll certainly run. Hope that's more useful if you dont wanna do gacha stuff like genshin!