* "A unique experience" is grammatically correct if you are referring to one specific experience that is unique.
* Example: "Going on a safari was a unique experience."
* "An experience" is grammatically correct if you are referring to any experience in general, regardless of whether it is unique or not.
* Example: "It's important to have an experience of different cultures."
In short, choose "a unique experience" when you are emphasizing the specific and unique nature of the experience. Choose "an experience" when you are talking about experiences in general.