What is the correct pronoun for the sentence if anybody wants to go to that new restaurant they must make reservations a month in advance?

The pronouns in the sentence are correct: anybody and they.

Although the pronoun 'they' is a plural form and the antecedent pronoun 'anybody' is a singular form, it is actually an acceptable use since English has no gender neutral, singular pronoun for a person of unknown gender.

The only alternative to using the pronoun 'they' is using 'she or he' in its place, which sounds clumsy to some people.