I agree with your feeling about the word "that" in this sentence. It is definitely not a sentence an English speaker would use. Also, the word "experience" can cause some difficulty, as some of the comments indicate.
I would recommend the following sentence instead:
Describe an occurrence (or occasion) in which you went out with your friends and had a good time.
There are a couple of points that are noteworthy for ESL students here.
The word "experience" has several different meanings in English. One of them is something that happens to you that affects how you feel. In other languages, this may be translated to words that are equivalent to "occurrence" or "occasion", but in English these words aren't equivalent; "experience" is used to describe special occurrences that have a deeper effect. As an illustration:
- If you go out to a bar with friends after work, it is an event or an occurrence, but generally it is not described as an experience.
- However, if on your way out of the bar you find that your car has been hit by a drunk driver, and you are then busy with the insurance company for hours to fill out a report, convince them that it wasn't you, and get a replacement car, and then return home only in the next morning, then it is likely an experience - something that does not happen often, and that you will remember for a long time afterwards.
The words "that", "where", "when", and "in which", are used in sentences like this to create a relative clause. In a relative clause we descibe more specific details about the topic of the main clause. The words we use depend on the detail we want to add; think about the kind of question that the relative clause could answer:
We can use "that", "who" or "which" in a relative clause to add identifying or classifying information. For example: "This is an event which I will remember for the rest of my life". (which kind of event is it?)
We can use "when" in a relative clause to add time-related information. For example: "Tell us about that time when your car was hit by a drunk driver". (When did that happen?)
We can use "where" in a relative clause to add location information. For example: "This is the bar where it all happened". (where did it happen?)
If the question that the sentence could answer starts with "in what" or "in which", then we should use "in which" to open the relative clause.
In the case of the sentence you are asking about, I would say that the information you add about the occasion is not just time or place - it is the identity of the occasion, so using "when" or "where" is not accurate. The question that can be asked here is "In which occasion did you go out with your friends and had a good time?" - and therefore, the relative clause should start with "in which".