Here's the corrected sentence:
Of course, we had to try the specialty of the restaurant, otherwise we would miss part of the East Indian experience.
Here's why:
* "Of course" is an introductory phrase that needs a comma after it.
* "otherwise" is a conjunctive adverb that indicates a contrast or alternative. Conjunctive adverbs usually need a comma before and after them when they are in the middle of a sentence.
* "the" is missing before "restaurant" to make the sentence grammatically correct.
By adding the comma after "restaurant," you separate the introductory phrase and create a clear contrast between the two clauses.