Learn English – “In the east” VS “to the east”

1. Whenever you speak of East and West "meeting" you are echoing a once very famous poem by Rudyard Kipling, "The Ballad of East and West", which begins and ends

   OH, East is East and West is West, and never the twain shall meet,
   Till Earth and Sky stand presently at God's great Judgement Seat;
   But there is neither East nor West, Border, nor Breed, nor Birth,
   When two strong men stand face to face, tho' they come from the ends of the earth!

   Although it is unlikely that many of your readers will actually know the poem, the first line is frequently quoted and has become a generally known catchphrase. Here meet has just the meaning it seems you intend: to agree, to share a common outlook. We speak in the same sense of a meeting of minds.

   Note that you don't need the phrase each other—that is 'built in' to the verb.

2. Some points in the sense of some matters is idiomatic. (It's meaning #1 in the dictionary you link to.) But at some points is used of physical or temporal locations, which is not what you want. (After all, geographical East and West do meet at infinite points along the border which divides them!) We speak of agreeing or disagreeing on points, rather than at them.

3. Give hugs to each other has a domestic, sentimental ring which I think is in the wrong register for what you are saying. I suggest embrace instead—which is doubly appropriate because we speak of embracing not only people but ideas and attitudes, too.

I think what you want is something more like:

East and West do meet, and even embrace, on some points.

Technically both are correct, but the second version is clumsy- and unnatural-sounding.

Moreover, the structure for the second is not always replicable, whereas the first one is. Consider the following examples:

He sees three people a few hundred meters away.

He sees three of people a few hundred meters away.

Here, using an exact number does not work for the second structure.

Consider another:

He sees several people a few hundred meters away.

He sees several of people a few hundred meters away.

Again, the first structure works and the second one does not.

But the second structure is the only structure that will work when dealing with a word that is only ever a noun. Consider the following two sentences, both of which use the noun "number":

He sees number people a few hundred meters away.

He sees numbers of people a few hundred meters away.

The first is obviously wrong (but note that it can be fixed by converting "number" to "numerous"). And another example with a noun:

He sees group people a few hundred meters away.

He sees groups of people a few hundred meters away.

Both "number" and "group" are definitely nouns, and only the second structure works.

Now consider one last example where instead of using a number (or an undefined number like "several"), we use the word "couple," which can be either a noun or adjective:

He sees a couple people a few hundred meters away.

He sees a couple of people a few hundred meters away.

Notice here that both structures work and sound natural.

So let's return to your initial example. "Thousand" can be a noun or adjective. And like "couple" above, both of the structures you posed work. The second structure is less desirable, but it's technically accurate.

These aren't absolute rules. The English language is treacherous and rarely do the "rules" always apply. But I'd conclude with this: use the first structure, except when using a word that is only ever a noun, when you should use the second structure.