Russian Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Russian language. It only takes a minute to sign up.Sign up to join this community
According to paragraph 184 (non-declining nouns) of the Short Russian Grammar (direct link - in Russian), foreign-language toponyms that end in vowels other than -а and -ы do not decline.
Hence, you'll get:
You do often hear в Хельсинках, however this usage is colloquial and is not grammatically correct. This is just an analogue of the declension of Russian toponyms with similar ending. Compare the above with:
Toponyms which calque plural from the language of origin do decline as plurals in Russian: в Афинах / Кумах / Каннах / Сиракузах, just the same as native Russian toponyms in plural: в Мытищах / Химках / Чебоксарах
However, Хельсинки is not plural in Finnish and hence not plural in Russian.
So it's a singular noun, and as any singular Russian noun ending in -и, is not declinable.
Correct form would be в Хельсинки.