My friend Melissa and I_a party. Would you like to come?

The correct answer is 'are going to go to'. Melissa and I are two people, so we need a plural form of the verb 'to be', which is 'are'. Then, we need the phrase 'going to go to' to express the intention to go to a party. My friend Melissa and I are going to go to a party. Would you like to come?