We're skipping ahead a little, because I think that while Gugs might be good monsters to use, they're also not that complicated. I might come back and do them and Mi-Gos, but I think this one is potentially a really interesting one to look at.
Elder Things appeared in In the Mountains of Madness, initially found by the antarctic research team in an inert state. Weirdly thought to be plants rather than animals, the explorers eventually find a massive subterranean ruin of a city created by the Elder Things millions of years ago. The Elder Things created the Shoggoths (oh, another thing that I actually skipped) to use for labor, but the Shoggoths rebelled and brought an end to their civilization. If memory serves, the Elder Things are later discovered to have not been dead, and they kill some of the researchers in an apparent attempt to learn about these new "human" creatures, but that's not really the focus of the terror of the story.
The Elder Thing stat block is a Large, CR 14, chaotic evil aberration. While they only have an AC of 16, they also have resistance to bludgeoning, piercing, and slashing damage, as well as psychic, and full immunity to lightning damage. They have a little over 200 HP. They aren't legendary monsters, but I also think you probably don't want to use more than one of these in a combat - having them assisted by minions (perhaps Shoggoths, even) would make a lot of sense.
They also have a 90-foot fly speed with hover, so they can dive out of the air and back up pretty easily.
But let's talk about their actions, because that's what I think is really notable:
First off, their standard Soothing Tentacle attack (reach 10 feet) does psychic damage and automatically charms anyone it hits. With a +10 to hit, that's going to hit pretty frequently. They make two of these attacks, and then they can do Psychic Skewer.
Psychic Skewer is one of the two really nasty abilities: a target makes a wisdom saving throw or take a bunch of psychic damage (though save for none,) but if the target is also Charmed (which can be pretty easy to impose with Soothing Tentacle,) failed save also means getting 1 level of Exhaustion and also being Stunned as long as they remain charmed (the tentacle only charms for one round, but repeated tentacles could stun-lock a PC).
Now, I think we need to parse this: the phrasing is "If the target has the Charmed condition, it gains 1 Exhaustion level and has the Stunned condition while Charmed." So: here's the question: does the Exhaustion also only last while the target is charmed? Or is that only the Stunned condition?
I'd be inclined to say that the Exhaustion stays even after the Charm ends, in large part because you're already not really likely to make a lot of D20 tests while you're stunned (though you can still move while stunned in 5.5) but also because Exhaustion is one of those things that really starts to get scarier and scarier as it stacks up, and this monster is supposed to be (and is, I'd say) scary.
This one-two combo is, I think, the most remarkable thing about the monster, but it also has a recharge action, Mind-Scouring Spores. Only recharging on a 6, you'll probably only use this once in a fight. The ability sends out a 20-foot emanation that calls for an Intelligence saving throw. On a failure, you take a pretty massive amount of Psychic damage (half as much on a success). On top of that, for 1 minute, you take 3d6 psychic damage whenever you take the Magic action.
To remind those who haven't quite internalized 5.5 terminology, the Magic action is when you take an action in combat to cast a spell or use a magic item, or any feature that requires one. If you're casting a spell that takes a minute or more to cast, you have to take the Magic Action on each turn while you're casting it.
What's interesting, though, is that if you're casting a bonus action spell, this doesn't actually mean taking the Magic action, nor does a Reaction spell. Thus, a Sorcerer could get past this by using Quickened Spell (and then just, like, Dashing/Dodging/Disengaging with their action). Also, Valor Bards, Eldritch Knight Fighters, and Bladesinger Wizards can also get around this if they're just weaving their cantrips into the Attack action.
But to bring things back: the Elder Thing is already resistant to conventional weapon damage, which will do a fair amount to extend its 200ish HP, but then it also does this thing that can punish spellcasters (probably not with enough damage to be a real threat, but it adds pressure).
Here's what I will say, though: this could be a really frustrating monster to fight - stuns and even being charmed can mean effectively losing your turn in combat (at least if there aren't minions to fight). Loss-of-control stuff in D&D is something that I would really caution against overusing, given that this can mean going for a pretty long time without being able to really do anything in a fight. That, I think, is the main reason not to use more than one of these in a fight.
Lastly, they also have a bonus action they can use 3 times per day to cast Command, Detect Thoughts, Gust of Wind, or Nondetection (no spell components, because of course they're psionic).
So, let's get into how I'd use these.
Notably, they could use their "Eldritch Magic" bonus action to keep themselves under 24 hours of Nondetection. While this can prevent remote location, it can also prevent things like Detect Thoughts, Detect Evil and Good, and other ways for players to simply determine what they are.
And thus, I think we could play with the idea that the party might find one of these just sitting there, inert, like in the story, unclear as to what the thing is.
There's an imperialistic quality to their description - not only did they create Shoggoths as a kind of slave species, but they also have their powerful charming abilities to force others at least into non-aggression. They don't have any kind of Dominate Person-like power, but I'd say they might seek to coerce others into serving their purposes nonetheless.
This is really the classic "what am I even looking at" cosmic horror starfish alien (though notably in the original story, they're not actually alien, just one of several species on earth from a profoundly long time ago, which is true for a lot of the so-called aliens in Lovecraft). I think it would make sense for the party to find this in some large cavern that, actually, isn't a cavern but a long-eroded artificial structure in one of their cities. Maybe it has been in hibernation for millions of years, undisturbed until the party, or perhaps some NPCs who arrived before the party, had stumbled across it.
If you wanted to play a little fast and loose with the stat block (which I always encourage - a Lich doesn't have to cast Animate Dead over and over every day to maintain control of their undead army) you could even make their minions humanoid NPCs who have had their minds taken over by repeated "Soothing." It's up to you if the NPCs are too far gone to have their minds restored, or if you could perhaps gain some allies by Dispelling the charm effect on them.
I suspect that even as a solo monster, they might present a significant challenge simply because they can shut down players so effectively (though if you miss on your two attacks, it'll be pretty sad) though Berserker Barbarians or Devotion Paladins are going to pose a huge threat to them given that they'll be immune to the charming and thus stunning effect.
The very high flying speed does also mean that the Elder Thing can A: get to ranged characters pretty easily and B: escape from combat pretty easily if things aren't going well for them. An Elder Thing who does hit-and-run attack, trying to land some Exhaustion on the party over the course of the day, could be really terrifying (indeed, with Exhaustion, they could even harass a party over the course of multiple days if they can stack up two levels of the debuff in each attack. Then, 90 feet of fly speed and Nondetection will make it pretty dang hard for the party to actually track them down to bring the fight to them while they rest and recover.
Elder Things are the second-highest CR among the Lovecraftian monsters in Horrors Within, with only the Yithians being slightly more powerful (in theory). And I think given the impact of its effects, it'll remain a relevant monster all the way to level 20 (though don't expect a group of 20th-level adventurers to be quaking in their boots against just one of these on its own).