1. This is the restaurant where he had lunch with Susan.

2. This is the restaurant he had lunch with Susan.
(Is #2 correct? 'Where' is missing in
#2.)

3. Look at the hospital where he was born.
4. Look at the hospital he was born.
(Is #4 correct? 'Where' is missing in
#4.)

5. This is the place where we played together.
6. This is the place we played together. (Is #6 correct? 'Where' is missing in #6.)

2 and 4 and 6 are incorrect. The word "where" is needed.

Those sentences could be OK, though, if you add "in" at the end of the sentence. Adding "in" at the end is bordering on non-standard English, but is acceptable these days in speech (but not in formal writing!).

I agree with writeacher

1. Both sentence 1 and sentence 2 are correct, although there is a slight difference in meaning. In sentence 1, the word "where" is used to specify the location of the restaurant. It implies that the restaurant is an important part of the story and the focus is on the restaurant where he had lunch with Susan. In sentence 2, the word "where" is omitted, and it implies that the main focus is on the fact that he had lunch with Susan at a restaurant, rather than specifically emphasizing the location.

3. Sentence 3 is correct. The word "where" is used to specify the location of the hospital where he was born. It is indicating that the hospital is important in the context of the sentence.

4. While sentence 4 is understandable, it is grammatically incorrect. The correct sentence would be "Look at the hospital he was born in." In this corrected version, the preposition "in" is used to indicate the location of his birth, as opposed to using the word "where".

5. Both sentence 5 and sentence 6 are correct, but they have slightly different meanings. In sentence 5, the word "where" is used to specify the location of the place where "we" played together, indicating that the place is important to the story. In sentence 6, the word "where" is omitted, and the emphasis is on the fact that "we" played together at a place, without specifically focusing on the location.