How do you answer con quien te gustaria ir a una fiesta?

That depends on who you want to go with, you are being asked who would you like to go to a party with, so if its the person asking that you like you say "Contigo si te quieres" meaning with you if you want. If its some else the say "Yo prefiera se VA con "name of the person" or you can use Prefero instead of Yo prefiera.