Neither you nor I are going to the show, or, Neither you nor I am going to the show
In Garner's Modern American Usage (2009), we find the following description:
1 when both subjects are singular, or when the second alternative is singular, use a singular verb
2 the verb "precisely" matches the form of the second verb.
And he adduces the actual real-world usage
Neither Barton nor I am saying that equities aren't a great long-term place to be.
from Fortune magazine, 1997.
Neither you nor I am going to the show
is the preferred sentence in formal writing. See also this ELU answer.
I am not telling you what to say. I am saying that when writing a formal paper, it is best policy to follow a style guide (such as Garner's). If you are not writing a formal paper, you can use other alternatives.
There are other examples in which the verb agrees in form with the closest noun. I'll edit the answer to add these when I have the opportunity.
Neither...nor (from MyEnglishPages.com)
When using either/or and neither/nor, note the following rules:
1. If both elements are singular, then the verb is singular too.
Neither Leila nor Nancy is going to write the report.
2. However, if one of the elements is plural, then use a plural verb.
Neither the teacher nor the students were in the classroom this morning.
The pronoun you is normally considered as plural. So, Neither you nor I are going to the show is the correct sentence.