Long time no see

Hi. I didn't write notebook for a long time but I had an amazing time.
I travelled two countries. Korea and UK.
They were very nice. I went to London alone. It was good experience :)
There are many countries I want to go.
It is interesting to know different people and cultures :)

I will go to Seoul again next month with my friend. So exciting!

Long time no see

Hi. I don't didnt write notebook for a long time but I had a amazing times an amazing time.
I traveled two countries. Korea and UK.
They were very nice. I went to London alone. It was a good experience :)
I have many countries I want to go to.
It is interesting to know different people and cultures :)

I will go to Seoul again next month with my friend. So exciting!

Long time no see

Hi. I don't write(haven't written in my) notebook for a long time(,) but I had a(an) amazing times.
I(have) traveled(travelled) two countries.(, both) Korea and UK.
They were very nice. I went to London alone. It was good experience :)
I have many countries I want to go.
It is interesting to know different people and cultures :)

I will go to Seoul again next month with my friend. So exciting!

Very well done!! Just a few small gammatical errors but the reader can easily understand what you are saying. Where I corrected your full stop and replaced with the word "both" is not an essential correction but is a more frequent way of writing this sentence. Also you have a choice of using "haven't" or the full words have not. You could also say I didn't write... but it is not considered good grammar.

Keep up the great work!