I am looking forward to ___________ on a vacation next month.

The correct answer is "going." In this context, the phrase "looking forward to" is followed by a gerund, which is the -ing form of a verb. This is a grammatical requirement in English; after certain phrases or prepositions like "look forward to," the verb must be in its gerund form.

Using "going" maintains the structure and intent of the sentence, clearly expressing anticipation for the future action of going on a vacation. The other choices do not follow the grammatical rules associated with the phrase. "Go" is the base form of the verb and does not fit after "to." "Be go" is not a correct verb form, and "going to go" introduces unnecessary redundancy without aligning with the grammatical expectations after "looking forward to." Thus, "going" is the appropriate choice to convey the intended meaning correctly.