Region: Middle Earth
My personal opinion on the matter is something close to Lindon-Rivendell's, but with less supernatural.
First of all, it must be noted that there exists the version of the old world (First Age) existing in a flat world (which turned to a sphere after the events of the Second Age where Numenor got flooded) and also existing in a spherical world (although is not the story in the Silmarillion, it does appear in The History of Middle Earth, mentioning that the flat world was just an old legend based on true events but told by men of the past and transmitted through generations).
Most texts, however, do treat the world in the First Age as flat but that got warped into a sphere by Eru once bits of it were removed (like Valinor), and from here stems the dimensional portal talk or its position in outer space - as you could only access Valinor via some magical route since its no longer physically on the sphere world (which now contains only Middle Earth, from one side of it to the other side of it now pulled and linked together).
With that out of the way, some more to add here.
Secondly - Valinor, or the Undying Lands, were a part of the continent of Aman. To the South of Valinor were some tricky places (place of Ungoliant the spider) and to the North of Valinor were some icy realms. Valinor, in itself, was protected to the North, South and to the East (since in the West was the end of the planet) by some very, very, very tall mountains called the Pelori (which got even taller at one time), raised by the Valar to protect their little part of the world. So Valinor, which existed in the continent of Aman, was fully encircled by unpassable mountains (they were tall, very slippery and very sharp / perpendicular). However, there was a small passage made through them, near the coastline, so you could enter or exit Valinor through there. From there you could sail on or you could just move through the coastline to the South or to the North (many elves actually resided on the coastline of Aman and not really inside Valinor).
Thirdly - At the start of the First Age, Valinor was on the same "planet" with what we know as Middle Earth at the start of the world. It was off to a side, just like the tectonic plates of our own Earth moved the continents around in our own distant past (or rather splitted the big chunk of mass into the continents of today). So, Valinor was cut off from the rest of the known world, but it was not 100% removed like an island, as it was linked to the extended Middle Earth (including Beleriand) at the top by a path of dangerous ice, Helcaraxe. When they fled Valinor, Morgoth and Ungoliant crossed this icy path from the north of Valinor and reached Beleriand and Middle Earth, but so did a large host of elves when they left for Middle Earth, so this shows that it was possible to cross back and forth from Beleriand to Aman (the continent hosting Valinor) - as an alternative route to the ships sailing the ocean.
Fourthly - In the Second Age, the whole part of Western Middle Earth, which included Beleriand, got sunk, and so the icy path connecting Aman to Middle Earth was removed and the continent that had Valinor was now actually an island. The way to reach it was, always (if I am not mistaken), via the sea route directly for the passage carved into the mountains near the coastline. If one is to notice the sea route, you can imagine it like departing from the the coastline of France and towards the bottom part of Argentina (so it was down to the South and towards West). Moreover, in the Second Age, in the front of the passageway into Valinor, a number of islands appeared, all covered in some very dense mists and home to treacherous winds and dangerous rocks to destroy ships and hallucinogenic and aenesthesic airs to incapacitate living beings. These acted as a layer of defense against those that wanted to reach Valinor but were not elves or worthy to enter / find Valinor.
With the background set forth, unless I am mistaken in what I wrote above, now comes my addition to the topic and what I view as exploitable gaps.
1) In the Second Age, one could also sail due West directly and reach the icy dangerous realms of Araman (which was the Northern part of Aman). It is challenging and probably extremely difficult, but so is sailing through misty treacherous islands set to destroy your ships and put you to sleep. And if the icy realms to the North are too dangerous for your ships, you could still sail close and reach the Southern part of Araman, and from there you could simply walk close to the mountain edge of Valinor until you reach the mountain pass near the coastline and from there hop into Valinor.
There is some indication that some Numenorean refugees at the end of the Second Age actually made it to these Southern parts of Amaran in their quest to find Valinor, so it is possible.
What can stop this "gap" from being super-exploitable is the presence of extremely strong sea currents, dragging all ships to the South. That would explain the South-West route taken by elves sailing in order to reach the mountain gap into Valinor.
2) Now we're at the end of the Second Age, where the Valar were fed with the Numenoreans trying to attack them and called on Eru to sink their island and cut off Aman from the rest of the Middle Earth (which turned the world of Middle Earth into a sphere). I view this, to some extent, pretty much in tune with The History of Middle Earth and say that the world was never flat to begin with but it was just the history told by sages to some that had less brain power than them so they can understand difficult and confusing notions if presented in simple terms (like you would explain string theory to a child). So, after the events at the end of the Second Age, I believe that Aman is still there but is unaccessible due to extremely strong currents that now move from West to East, one that goes from West to North-East and one that goes from West to South-East, barring all movement except a peculiar route where the two currents almost meet and where there is a place like the eye of a storm (of calm) that the elves know about and can exploit in order to reach the mountain pass of Valinor. Simple as that, with no supernatural dimensional portals involved.
Feel free to correct me or to add more information!