In an effort to spend more interestingmake the most of my time during my business trips, I usually have a tight plan after getting offtry to plan a few things to do after work.

Your original was understandable, I've just made it 100% natural for your reference.

When I went to Warsaw, in Poland, I always left the office at 5 pm and took a walk to the famous museums.

I think you need the second comma because this is additional information.

I visited two museums near the office ;: the War mMemorial mMuseum and the Train mMuseum.

The semi-colon separates clauses (e.g. 'There were two museums close to the office; I went to both') honestly it's not common to see semi-colons in casual writing. Most people don't really know how to use them.

For your sentence, a colon is correct.

The names need to be capitalised, since they're proper nouns.

And II also went to the old town of Warsaw, where there aris the Warsaw nNational mMuseum, the Marie Curie mMuseum and the Chopin mMuseum.

It's not absolutely impossible, but it's generally considered bad practice to start a sentence with 'and'. This is something every child is taught at school so it's jarring to see.

Even though you're talking about multiple museums, you need to use 'is' not 'are', since there's only one Warsaw National Museum etc. What I've put above is basically short for: 'There is the X Museum, there is the Y Museum and there is the Z Museum'. Alternatively you could say: 'There are the X, Y and Z museums'. Hopefully that makes sense!

When I visited Calgary, in Canada, I went to the central avenue where you can see charming tram is operatings.

It's best to put 'in Canada' between commas because it's additional information.

'Operating' has a technical / formal feel which doesn't fit your tone.

IOn the avenue, I could buy historyou can buy books about Canada, got a stamp thatian history and stamps with Queen Elizabeth on ithem.

It's 'on' the avenue. I can only apologise for this really confusing aspect of English.

If you did buy some books, it's best to say 'I bought books'. If you didn't, it's best to say 'you can buy books'. Saying 'I could buy books' just makes me wonder why you didn't buy them.

But I think, it is more interesting when I travel not by business trip but by my vacationIt's nice to feel as though I'm on vacation when I go on business trips.

There's no need to say 'but' because this is a conclusion, not a counterpoint.

I struggled to re-work your original into something natural so I've just replaced it.

In an effort to spendhave a more interesting time during my business trips, I usually have a tight plan after getting off work.

you could say spend more time, but you can't put another adjective after more if you're using the word spend.

I visited two museums near the office ; Wthe war memorial museum and the train museum.

you are talking about specific museums so use a definite article

And I went to the old town of Warsaw, where there aris the Warsaw national museum, the Marie Curie museum and the Chopin museum.¶
¶
or ¶
I went to the old town of Warsaw, where the Warsaw, Marie Curie and Chopin museums are.¶

Don't use "and" at the beginning of a sentence !

- You're giving specific examples of museums so you can use the word 'is' and use a definite article in front of all of the museums.

When I visited Calgary in Canada, I went to the central avenue where the/a charming tram is operating.

you need to use an article before tram - either 'the' or 'a'

In the avenue, I could buy history books about Canada,. I got a stamp withat Queen Elizabeth on it.

you either need a new sentence or add the word "and"

In Nanjing, China, I went to many shops related with teas and tea potteries.

it sounds more natural to say shops with teas

But I think, it is more interesting when I travel not byfor business trip but by mybut for vacation.

this sounds a bit more natural