The correct option is D to visiting
Let’s examine the sentence: “We're looking forward ____ the museum.” Option C is the correct answer as the use of the infinitive ‘to visiting’ brings together the expression, ‘looking forward to’ and the gerund, ‘visiting’ to complete the meaning of the sentence. The expression ‘looking forward to’ means hoping with joy for the event to happen and the gerund ‘visiting’ is used to refer to the ‘fact’ of visiting. The gerund always has the same function as a noun (although it looks like a verb). The gerund ends in ‘ing.’ Hence, Option C will bring out the correct meaning of the sentence. Options A, B and D cannot be used as they would render the sentence incorrect grammatically.