Is the location of Rivendell a secret?

Adding to the already mentioned points,

Ian Thompson mentions:

highly educated individuals such as Denethor would know of Rivendell's existence and its approximate location

We can assume that there are old maps showing the location of Rivendell. That's probably how highly educated individuals with shorter lives would know how to find it.

Technology in the Middle-earth is sparse. Those maps are probably old, few and stored at libraries of centers of knowledge or certain important lords. Peasants won't have access to Google Maps, or have access to a satellite image to see if there is more than ruins there now (which would have been useful to detect much earlier what was happening in Mordor, too).

Traders don't seem to pass by Rivendell, which makes the place unknown to most humans. Plus, even if the above-mentioned maps were available to those immigrants and poor people seeking refuge, they wouldn't know if there were still a city at such place, and they wouldn't know if they would be well-received. You ask knowing Elrond's personality and the life Bilbo lived there. We don't know if Elrond would indeed happily welcome anyone who appeared uninvited at the doors. Probably not hundreds of immigrants. At least not without them earning their living in some way, I think.

I see a certain appeal in traveling to Rivendell "in order to see elves". But when it's not a weekend trip, but months of travel, to a city you don't know whether it still exists, where you might not be welcome at all, and led by people who aren't even human (yes, it is racist, but those poor immigrants would probably have heard some frightening stories about elves¹). It's much easier for those poor people to move to the next human town (if moving at all), and continue their lives in poverty, but in well-known places and without adventures.

¹ And no, don't expect they would know -or understand- Elrond's ancestry, much less consider him half-human.

One thing that stands out in all of the books (and the movie, also) is that "the poor" in Middle-earth do not seem to ever have the "sense of entitlement" that they should get paid for merely existing - except at the very end of Return Of The King - and it's a sentiment that is expressed by Sharky's Men and by some squinty eyed almost half-orcs at the Prancing Pony, earlier in the book. Nowhere in the book is it mentioned that anyone begs for money - I think there's a few mentions of better off people helping poorer people - but the general notion is everyone pulls their weight. Look for example at the depiction of Samwise's father the Gaffer. The book says he ran the garden at Bag End until he got too old and was then setup in a small "efficiency hole" in Bagshot Row and then later New Row when Saruman had Bagshot Row dug out. There does not seem to be any mention of the Gaffer working, other than raising a few vegetables in his own little bit of garden. Yet he is able to hold forth at the local inn and drink a few pints.

The setup is almost identical to how older people in the village are handled in Downton Abbey. Later in the show when they are talking about raising the farms agricultural output they specifically state the need to build little efficiency cottages and move the farmers who are too old to work the farms to them. That happens to Mr. Carson as well. Clearly this must have been rather common in England at least in the small villages and farming communities - as farmers got old and unable to work they would be moved off to efficiency cottages in the village and given a small pension, and would perhaps buy a bit of meat of fish with it on occasion to supplement gardening output and I think Tolkien certainly intended the same model in Hobbiton. In Middle-earth, everyone worked, everyone was useful, from the old to the young, and those unfortunates who perhaps were victims of accidents or wars and were unable to work, were taken care of by their communities. Nobody is addicted to drugs, very few are mentally ill, and criminals existed as bandits in The Wild. The various jails and stockades were places to put young pups or others who might have gotten too drunk and rowdy at a party and torn up a garden, or stolen mushrooms, for a day or so to teach them not to do it again. There's no mention of mass murderers for example and theft is rare.

I'll also mention that while there is a LOT of mention of EATING in LoTR there's NO mention of...well...what happens to the digested food down the chain, you might say. Nobody goes to the bathroom, the cities do not appear to have pressurized running water. There are horses everywhere including running throughout the cities but no mention of horse piles in the street. Google up "The Horse-world of London By William John Gordon" a free ebook to see the realities of running a city dependent on draft animal labor.

In summary, this masses of refugees, immigrants and poor people simply NEVER exists in the Middle-earth universe. When mass migrations of people happen they bring huge amounts of "stuff" with them, and plunk down in a new area and setup shop as though nothing had happened. Every bit of Middle-earth's depictions of daily life living is HIGHLY idealized and not consistent with behaviors of real people in the real world. Boromir wanders long forgotten roads and meets many people but did he have a huge purse stuffed with gold coins to pay his way or did he camp out everywhere, spending days to hunt down deer and gather wild vegetables for his diet?

So the answer to your question is - it's moot. There are no masses of poor refugees who would get a better deal moving away from their communities. Men in Middle-earth do not act like humans - in the real world with humans if you give them an empty area they have large families until that area is built up - in Middle-earth you have have thousands of acres of tillable land that was once tilled by men, remain empty for a thousand years after a war. In the real world curiosity causes some men to seek out buried treasure, so the idea of a former city being abandoned stimulates floods of treasure-seekers to look for it, in Middle-earth when something as valuable and large as the Master Stone in Osgiliath is hidden and lost after a war, nobody seeks for it. Even after the War of the Ring is over, and Sauron is defeated, and it's safe to look into a Palantir, it does not seem to occur to the King to use his Palantir to seek out where the rest of them are and dig them back up - particularly to seek out the master stone in Osgiliath. In fact, long after the war is over Osgiliath remains abandoned even though it is the optimal location for a capital city due to it's position on Anduin. Moria is also never discussed in the later Appendixes even though the killing of the Balrog and destruction of the Orcs would have open it up for treasure hunting.

Elves and Dwarves do not act like people, that is acceptable as they are other species. But Middle-earth men do not act like men. If humans in Middle-earth were told about a famous Elf city named Rivendell it would have no hold on them they simply wouldn't care.

In addition to the points mentioned in @Ted Mittelstaedt's answer, you need to understand that, unlike our modern world, Middle-earth is not vastly over-populated. There are large areas that are empty of any human (or Elvish & Dwarven) population.

So what human populations do we have that are anywhere near Rivendell? There are the Men of Bree, a small population apparently quite happy and prosperous where they are. There are the Rangers (Aragorn's folk) who are wanderers in the rest of Eriador, and who do sometimes visit Rivendell.

On the other side of the Misty Mountains, there are the Beornings, who likewise seem to be quite safe & happy where they are. On the other side of Mirkwood (a perilous journey) there are the Men of Laketown, who apparently live happily in association with the Wood Elves and (now that Smaug is dead) with the Dwarves of Erebor, and have trade with Men and Dwarves of points east and south.

To the south and west, the land seems to be completely unpopulated until you get close to the south coast, some of which belongs to Gondor, some to various populations of Dunlendings. But Boromir doesn't seem to meet anyone on his journey north through those lands, nor does the Fellowship meet anyone until they go through Moria. And even on the other side, they only meet Orcs until they reach Lothlorien.

Which leaves Gondor itself. There were (presumably) refugees from Ithilien when it was overrun by Sauron's forces, but they were accommodated within the lands of Gondor west of the river. There was plenty of room: Gondor could allow the people of Rohan to settle in the western part of their land without (apparently) discommoding anyone.

So basically your refugee & immigrant situation simply doesn't exist. Unlike the modern world, there really aren't any great disparities in wealth between areas, so no one has motivation to travel great distances to seek better economic conditions. (And if they do, they probably go to Minas Tirith or Laketown.) If they're driven out by war, they don't have to go far to find empty lands in which to settle.

The only indication I'm aware of that Rivendell's location is a secret is the following passage from The Hobbit:

...and into that valley came no evil thing.

However, that can be explained by having other effective forms of security.

There's no mention of it having Gondolin-level secrecy.