Answer:
We wanted to visit the museum while it was featuring a traveling exhibit about the Titanic.
Step-by-step explanation:
Adverb is the grammatical class of words that modifies a verb, adjective or other adverb. Never modify a noun. It is the invariable word that indicates the circumstances in which the verbal action occurs. The adverbial clauses have the same function as an adverb.
On the basis of this we can conclude that the adverbial clause "while it was featuring a traveling exhibit about the Titanic." is modifying the infinitive verb "to visit". Moreover, this is the only phrase among those that were shown in the question, which has a verb in the infinitive form.