"We do not like this exhibition."
Translation:Нам не нравится эта выставка.
That does sound a bit funny, as if you were a frequent visitor. Remember, любить is not a one time action. If you like or do not like a particular object with любить it means that you use that object on a regular basis, which makes it possible to pass an overall judgement on your experiences with it.
I don't believe that нравится is reflexive, because the subject of the verb is the thing that is liked, and the pronoun refers to the person liking that thing - the format doesn't reflect the action of the verb back on the subject, but onto a dative pronoun.
The singular forms of the verb are:
Ей, нам, вам, им нравится
The verb doesn't change whatever the person or number of the pronoun is. The verb only changes if the number of the subject (the thing(s) liked) is singular or plural.
That's simply not a reflexive verb.
The sentence "Нам не нравится эта выставка." literally says "This exhibition is not liked by us.", which makes the verb reflexive. "Нам" is an indirect object (dative) and "выставка" is the subject. My dictionary refers to this verb as "class 4a imperfective reflexive".
Нравится is literally a reflexive verb, structurally speaking. It is another matter entirely what the verb means: Russian "reflexive" verbs have a lot more uses that just performing actions on the subject itself. The only thing in common is that the verb is intransitive, i.e. cannot have a direct object, and it truly holds (save for very few exceptions like бояться).
John204: If your sentence construction were correct (and according to Shady_Arc’s above post, it is not), then you would still need to put the object in your sentence into the accusative [objective] case, not the nominative as you have it in now. I’ve also found it to be helpful to read the entire thread before posting a question, as more often than not I’ve found it to have been already answered.