I am not sure whether the two sentence makes sense in term of grammar and semantics.
Can you give me a hand with checking them
Thank you for your help.

The most effective method of learning is to integrate reading,talking,doing and listening to somehing into a combination of learning.

Going sightseeing in the United States gives me a opportunity of immersing myself in the English speaking environment and knowing the real American culture.
1 2
a) "The most effective method FOR learning (a language) is to integrate listening, reading, speaking and practicing into a form of study combination."

b) Going for sightseeing in the United States will give me the opportunity of immersing myself in an English-speaking environment and getting to know( getting acquainted with) real(actual) American culture.

Perhaps, others here may correct them better.
The four skills are listening, reading, speaking and writing, so if you do not insist on practicing (doing), I would suggest writing instead.
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Hello D.

'method of' seems more idiomatic than 'method for' in this context.

How about:

1. In learning a language, the most effective method involves the integration of listening, talking, reading, and writing.

2. Traveling throughout the United States provides opportunities to immerse myself in the environment and culture of English-speaking Americans.

(Semantically speaking, I suppose, the thought expressed in no. 2 is a little too obvious, although traveling for some individuals might have less to do with a desire for immersion, than with a need to escape routine.)
b) Going for sightseeing

In British English we say "going sightseeing". The addition of "for" just sounds wrong to me. The only time we would use "for" is in: "going for a sightseeing tour".

However, it may be correct in Am.Eng.

For example, the Americans say (e.g.) "I went to visit with my aunt", whereas we Brits would say: "I went to visit my aunt". We would never say "with" in this context (because it changes the meaning).
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Eimai Anglos,

Which would you deem to be the right answer to the following question?

Q. What are you going to America for?

i) I am going to America sightseeing/shopping/studying/working/etc.
ii) I am going to America FOR sightseeing/shopping/study/work/etc.
Interesting, I would probably say ii).

However, you've altered the sentence structure. I would never say "Going for sightseeing in the United States". So I guess it's dependent on the context and sentence structure. The difference lies in the choice of verb: to go for or to go to.
Think I'd say:

iii) I'm going to America to do some shopping/sightseeing
iv) I'm going to America to study/work

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