I've been playing for nearly a month now and I feel like I've completed less tan 10% of what the game has to offer; much of the map is still blank, and I'm only at the second temple.
The game is unbelievably huge. But unlike so many really big games, pretty much none of it feels wasted, there's always something to find or do no matter where you go, whether it's a cave, a miniboss, or a falling rock that will take you up to a new sky island. It's not just big, it's dense too, packed to the brim with content, almost all of it top notch.

I'm still in the depths, went in there for the first photographer quest and never left lol. I don't have much time to play anyway, slowly plugging away at exploring. Half a dozen light roots found so far, so many more to go. The central mine complex was pretty cool, I got the miner's pants and chest so far, dunno where the hat is (I assume there will be 3 items). The light it emits is just enough not to walk blindly off a cliff. Which begs the question, where are those abundant light seeds? I'm using them very sporadically, just a handful left, thus inching my way to light roots in the dark.

Combat is kinda trivial so far. Shoot a couple muddle buds into a camp and they take care of each other, then take the left over(s) out with bomb flowers. There are lots of those around. I still only have 4 hearts, so basically any hit is instant death now. Dying restores 3 hearts gloom free, with 4 hearts that's pretty much full health again. I did manage to defeat the master of the Yiga clan, so now they're after me again lol. I wonder how long they'll harass me this time haha.

Anyway the depths are glorious, mysterious, dark and all new ground to explore. There are bosses I can fight but not worth the resource drain. Bows break very quickly shooting bomb flowers at a mini boss and the weapons I have barely take a pixel off their health bar. Clearly I need to level / gear up first. Still no fast travel use, haven't tried ascend either, I'm fine down here, just walk around the mini bosses. I would like a bigger battery though as I found a blue print for a flying machine yet with the original battery it only lasts 20 seconds. No clue yet where to upgrade the battery but I have gathered lots of Zonaite for it.

One thing that kinda irks is I found these headlamps so I figured put one on a shield and I have a re-usable torch. But for some reason using my shield light simply as a flash light very quickly breaks the shield :/ Anyway back to the depths, mapping the underground one step at a time.

You upgrade the battery in a specific cavern inside the tutorial archipelago, it's the cavern where you wake up at the start of the game. There is a shrine in front of it. I think you will need fast travel to get there

Welp, I've continued my adventure towards some of the sky islands in the south of central Hyrule and found a shrine quest there. Also found a mysterious sky island build different from the others with a written plaque with ancient hyruliean on it. Don't know what the purpose of this'll be.

After that, I jumped right beside the Colosseum Ruins explored some places found more stuff than I expected and a bit later I actually found the most impressive cave yet ... Which led me to find a rare piece of equipment it seems. How freaking awesome was that. And this wasn't even part of the Depths yet, which I haven't explored yet ...
Although, I found a well that was infested with the gloom, jumped in it, realized it was an entry to the Depth and proceeded to die because I couldn't hit the bottom fast enough since I couldn't see shit inside it because of how pitch black it was.

Makes me anxious at exploring the Depths now if this is going to be this intimidating to go through ...

Caves - there's crapload in almost everyone of them. And those little frogs in Depths drop seeds when you kill them (not sure what they're called, they usually come in packs).

You can do it just outside lookout landing as well.

There's another spot where you can upgrade your battery next to lookout landing.

I found some balloon things in the depths, dunno if they can carry me up to sky islands, haven't touched them yet. Anyway thanks @pikashoe and @Kakadu I assume the balloons will carry me back up to Hyrule so lookout landing is in reach without fast travel.

I guess those caves are in Hyrule and on Sky Islands? I'm in a giant cave (the depths) and no seeds there, just the few that drop from enemy kills. The light roots spread light pretty far anyway, plus I have 2 glow clothing items and plenty glow food and elixers now. Just using a bright bloom seed for light up camps to see what I'm dealing with. Too much fun exploring the Depths, I've wandered quite far from lookout landing already. No clue yet if it's all connected, it's kind of a big maze down here with thin ish walls separating sections.

Yiga clan seems to have subverted all NPCs down here, each one I talk to turns into a Yiga fanatic after they've delivered their message lol. Fast teleporting bastards, at least they're easy to kill so far.

Beat the water temple; the low gravity and giant moving spheres of water were hella cool.

The games is so ridiculously more-ish in that I always feel like I wanna keep playing just to get to that next shrine on the horizon, complete that side quest, or explore that cave. Every thread leads so elegantly to the next like a giant tapestry.

Shrine hunting currently, my goodness the shrines are so much better than BOTW (and most of those were good)