First of all, you should write 'students' in both sentences, not "student". Also English needs a capital E because it is the name of a language.
You are right; both sentences are correct but the meanings can be different. You are also right in saying that the words in red describe the students.
In the first sentence, the "place" is a good place to study English.
In the second sentence, the "place" may be a good place to study English, but it could be a good place to live at or to buy books at. The place to live at or to buy books at may be very close to the English school, so you can say that 'I think it's a good place for students studying English (at the school to live at/buy books at).'
Please use smaller letters, as it will be much easier to read.