"The park is not there."
Translation:A park nincs ott.
It's a correct answer, and your teacher was correct. Nem ott van a park is saying nem ott, which is fine. It's not saying nem van. In other words, it's the ott is being negated, rather than the verb.
Nem ott van a park is like, the park exists (the verb van is positive), just "not there". It would be consistent to continue the sentence with something like Nem ott van a park, hanem itt a múzeum mellett. (The park is not there, but here by the museum.)
A park nincs ott is just like, the park is absent, doesn't exist (nincs).