Yesterday, I visited a shrine yesterday with foreign friends I had met at a language exchange meet-up on the New Year's Eve.

We call the first visit of the year "Hatsumoude"."

In English, punctuation marks usually are kept inside the quotation marks when writing, is it the same in Japanese?

We stood in a long line for a prayer place andthe place to pray; it took around an hour to get thero the front of the line.

You can make two sentences or use a semi-colon (that's up to your style)!

I wanted to buy a lucky charm but gave it up because I found I would have to stand in another long line.

We joined a party after that and wereAfterwards, we went to a party and drianking until very late at night.

I gotwas a bit haungover today.

ButHowever, I was happy that we had a heart-to-heart talk because of beer or any other alcohol drinks unlike, because of the beer and alcohol drinks, we were able to have a heart-to-heart talk, which doesn't happen at language exchange meet-ups.

Any of the corrections work because commas or "," in English introduce clauses that can be put at any point in the paragraph.

It was an that moment, I was glad that I have been studying English.

Until now, I had shied away from joinattending thisose kinds of party so far but will try to join at timesies, so I hope to participate more in the future.

I visited a shrine yesterday with foreign friends I had met at a language exchange meet-up on the New Year's Eve.

I wanted to buy a lucky charm but gave it up because I found I would have to stand in another long line.

We joined a party after that and were drinking until very late at night.

stating "at night" is okay, but "very late" usually implies "very late at night"

I gotam a bit haungover today.

you get/have a hangover or you get/are hungover.
"a bit" + adjective or "a bit of a(n)" + noun.
"I am/was a bit hungover today"
"I got/have a bit of a hangover today"

But I was happy that we had a heart-to-heart talk because of the beer or anyd other alcoholic drinks unlikethat we don't get to have at language exchange meet-ups.

It was an that moment, I was glad that I have beenam studying English.

"am" sounds better to me, although "have been" still works

I hadve shied away from joining this kind of party so far, but will try to join at times.

If you use "had shied away" your next clause should be in past tense. Using "have shied away" allows you to use present and future in the next clause

I visited a shrine yesterday with (some) foreign friends (whom) I had met at a language exchange meet-up on the New Year's Eve.

Saying "...that I had met" would be okay, but it's not grammatically correct. If you want to put a word there, it should be "whom." ("Who" would also be natural, though not gramatically correct.)

We stood in a long line for a prayer placelace to pray, and it took around an hour to get thero the front of the line.

I wanted to buy a lucky charm but gave it up because I (found I) would have had to stand in another long line.

We joinedwent to a party after that and were drinking until very late at night.

I gotwas a bit haungover today.

But I was happy that we had a heart-to-heart talk, unlike at language exchange meet-ups, because of the beer or anyand the other alcoholic drinks unlike language exchange meet-ups.

It was an that moment, I was glad that I have been studying English.

I had shied away from joingoing thiso those kind of party so faruntil now, but will try to join at timesin sometimes from now on.

I visited a shrine yesterday with (some) foreign friends that I had met at a language exchange meet-up on the New Year's Eve.

We stood in a long line for a prayer place, and it took around an hour to get there.

I wanted to buy a lucky charm but gave it up because I found I would havedidn't want to stand in another long line.

We joinedwent to a party after that and we were drinking until very late alast night.

I gotwas a bit haungover today.

It was a moment were I was glad that I have been studyingstudied English.

alternative

I had shied away from joinparticipating ing thisese kind of party so faries, but I will try to join at go sometimes.

alternative

I visited a shrine yesterday with foreign friends I had met at a language exchange meet-up on the New Year's Eve.

We stood in a long line for a prayer place and ilace to pray. It took around an hour to get thero the front of the line.

We joined a party after that and were drianking until very late at night.

Saying "at night" is ok, but it sounds more natural without.

I gothad a bit of a hangover today.

Or if you still have it:

I have a bit of a hangover today.

The previous correction is ok, too.

But I was happy that we had, unlike language exchange meet-ups, we could have a heart-to-heart talk because of beer or anyd other alcoholic drinks unlike language exchange meet-ups.

The previous correction is fine, too.

It was an that moment I was glad that I have been studying English.

I had shied away from joining thisose kinds of party so faries until now, but will try to join at sometimes.

I visited a shrine yesterday with foreign friends I had met at a language exchange meet-up on the New Year's Eve.

We stood in a long line for a prayer place, and it took around an hour to get there.

I wanted to buy a lucky charm but gave it up because I found I would have to stand in another long line.

We joinedwent to a party after that, and were drianking until very late at night.

I gotwas a bit haungover today.

ButHowever, I was happy that we had a heart-to-heart talk because ofthanks to the beer or anyd other alcoholic drinks, we were able to have a heart-to-heart talk, unlike at language exchange meet-ups.

It was a moment at which I was glad that I have been studying English.

I had shied away from joinparticipating ing thisose kind of party so far butup until then, but now I will try to join at go sometimes.