Hiding in plain sight
The Collector a.k.a Taneleer Tivan can be seen in MCU and he is actually a much more powerful being originally in comics than portrayed in the MCU
"I present to you, Taneleer Tivan, the Collector!" ―Carina (in Guardians of the Galaxy)
MCU wikia explains about collector as follows,
Taneleer Tivan, also known as the Collector, is the keeper of the
largest collection of interstellar fauna, relics and species in the
galaxy, operating from the Knowhere port installation. Through his
dealings with Asgardians and the Guardians of the Galaxy, he was in
possession of one of the Infinity Stones and was nearly able to obtain
a second stone. However, this caused Thanos to attack his museum
seeking the Aether.
it further explains how Tivan got the stone in the first place,
In 2013, two Asgardians, Sif and Volstagg, arrived at Tivan's museum,
bringing with them the Infinity Stone known as the Aether, which had
been recovered by Thor after his battle against Malekith on Earth.
They gave it to him believing that it would be safe from other
parties. When Tivan asked why they did not keep the Aether in their
own vault on Asgard, they explained that they thought it would not be
wise to keep it on Asgard since another stone, the Tesseract, was
already on there; a notion that Tivan agreed with. As Sif and
Volstagg left the Aether in Tivan's care, Tivan remarked to his
assistant, Carina, that they now had one of the Infinity Stones in
their possession, and only needed the remaining five, hinting that
Tivan was already seeking the Infinity Stones. Tivan learned the
location Power Stone, which was contained inside the Orb and begun
working out a plan to obtain it for himself.
From an answer for a similar question in SciFi SE ,
MCU version of Tivan portrays him as just an
eccentric collector so far, the comics version has a personal mission
of collecting artifacts and subjects and keeping them safe so that the
Universe could be repopulated. Not only does Tivan have a personal
mission to keep all of these artifacts safe, he also has ten heavily
guarded museum worlds, as well as a ship that remains in hyperspace
almost all of the time to avoid being detected. Additionally, he has
"temporal assimilator" which can be used for limited time-travel.
There was a conversation between Thor and Star-Lord in Avengers Infinity War,
Star-Lord: "If it's with the Collector, then it's not safe. Only an
idiot would give that man a stone."
Thor: "Or a genius."
POV from Reddit
In MCU The Collector was a known buffoon - despite his reputable
collection of things, he was a joke across the galaxy. But then the
Asgardians realized that the one place nobody ever thought they'd keep
the reality stone was with a well-known doofus.
It's essentially the galactic version of hiding something in plain
sight, like stealing the Mona Lisa and hanging it a small town
community art museum, nobody would ever think something so valuable
would be in such a non-descript place with such an idiot guarding it
that they wouldn't even bother to look there in the first place.
I found another POV in reddit,
Personally, I felt the most important reason was that The Collection
had no intention of using it. Odin/Loki didn't trust having two
infinity stones on Asgard, so he probably wouldn't trust the Nova Corp
with it either, nor the Avengers, since Earth had two already.
So, Collector can be choosen for
Has the ability to protect a stone,
Would be willing to have a stone, despite it potentially putting a
bullseye on them.
- Can be trusted not to abuse it.
The Collector wants it for its rarity and collectability, not the
things he could do with it. He wasn't going to go try take over the
galaxy with reality warping power. So, he was a good choice. The only
question was his ability to safeguard it. Assuming no-one would find
out he'd been entrusted with it, and that the Collector had probably
collected a number of defence systems to protect his collection, he
was probably a decent enough choice.