レベルの高い高校って英語でなんて言うの？

You can use the word "elite" to describe any school that is considered high level.
It is often used in the US with ivy league schools, but it can also apply to any high level or hard to enter school.

• Elite high school.
• Elite university.
• Elite kindergarten.
• Elite school system.

"top level/ top-tier" means held to a high standard, above average, better performing school.

1. If a school has a great reputation, it infers that it is high quality.
2. If places are much sought after (in high demand), it infers that the school is high quality.
3. Incredible teaching staff = a high quality school.

The term "elite" means superior. Most private schools in the U.S. are considered to be the best in education or better than most public schools. We also use the term "top".
For example: This is the top school in the city.

There are many ways to describe an institution that has a high level of education or a good reputation.You called also use synonyms such as :

-esteemed
-prominent
-illustrious
-acclaimed

These synonyms are used to describe any place/institution/or person whose quality ,a reputation that is above average or is able to perform beyond usual expectation.

"High level" schools, it has many different names. Each country has a different way of naming these learning establishments.
"Private school"
"Independent school"
"Non-government school"