First a warning. This answer will contain spoilers for Kingdom Hearts 1, Chain of Memories, Birth by Sleep, and a few items from KH2. If you do not wish to be spoiled, then stop reading now
I've been giving this a lot of thought, and I've come to the conclusion that...
The grassy field is not on any known world
and here's why:
I'll be using these images throughout my explanations.
In the first picture you see the field in question. This pictures shows not only shows the path Sora is taking, but also a large area of the terrain. The field consists of a large expanse of rolling grassy hills with sparse trees. Even off into the distance there are no significant landmarks or changes to this that can be seen. The sky is a bright blue with pretty standard cloud cover.
Likely Candidate: Land of Departure
So, the biggest candidate for the world it would be on is the Land of Departure, as that is where Castle Oblivion comes from. However, by the end of Birth by Sleep, there is almost no world remaining. The world has been torn apart by the dark orb released by Master Xehanort and mostly the castle and shards of the surrounding area remain, similar to what happened on Destiny Island.
Now, one might guess that these pieces of the land had been sucked into the early versions of Kingdom Hearts that were forming (even though the two events are a ways apart and occur because of unrelated incidents), and therefore might have been restored once Sora closed the door, as were the other worlds. But, even if this were true, only pieces of the world could be restored since most of the rest of it had been transported along with the castle, so the countryside would still remain in shambles. And even if it hadn't, no terrain seen in the Land of Departure resembled these hills. The hills shown were much larger and steeper.
There is only one other terrain that has been shown and matches these rolling hills but it can be immediately ruled out: Destiny Island. Well, not the island itself, but the mainland where everyone lives. It was shown with Kairi in KH2 in short cutscenes and resembles these hills. But, at the end of of KH, we see Kairi end up on the island, so Sora cannot be there.
But then how do they arrive at Castle Oblivion?
I originally thought this was the single piece of evidence that they had to be in the Land of Departure. But, as I thought about it more, I realized that it didn't mean that at all. Castle Oblivion is no longer at the Land of Departure and is instead in the realm between, so it isn't like, even if it were at Land of Departure, they could just walk there.
And if they couldn't walk there from the Land of Departure, then the only other place that world could be is in the realm between. But we've seen many instances of the realm between and they all look very similar to the areas around Castle Oblivion, not like this giant field. However, if we entertain the possibility, we only need examine the images above. In image 2, you see the night sky from perspective of the grassy field. It is a deep blue color with some scattered clouds. On the right are two images of the sky around the Castle. As you can see, the sky is a much darker color, and is surrounded by very different clouds. Even if the terrain were to change that drastically, the sky would be unlikely to change (even with the KH universe). So, there is a high likelihood that these two places are not on the same world.
But probably the biggest piece of evidence in favor of this separation is this drawing by Naminé.
Naminé, throughout Chain of Memories and a bit into KH2, shows a large amount of control over Sora, and those around him. Here, we see a picture of Castle Oblivion, drawn by Naminé. Drawings are at least one way she controls Sora, and his environment, so it is highly likely this drawing brought Sora (along with Donald, and Goofy) to the realm between and to Castle Oblivion, which was already being used as a hideout. So it didn't matter what world the grassy hills were on, because they had the ability to bring Sora to them, regardless of where he was left.
So, all of this leads back around to the conclusion that this world is likely a one-off, plot filler world. At the end of KH1, Nomura stated he wasn't sure if he would get to do a sequel, so likely he left them in this field with some idea of what was next, but not a fully developed one. Once he had a direction, this area became only significant so far as it was where they already were and he needed a way to get them to their next destination. At least, that is one possible explanation for this not being a world we know anything about..