去出回 Where is it appropriate to use each So these three have always threw me through a loop  


去 - Qù - Means to go to a place  
出 - Chū - Means to go out
回 - Huí - Means to go back


The only case I know to not use 去 (Qù) as a way of going somewhere is when saying your going home at which point you use 回 (Huí)

How can I identify a situation where each version of 'to go' is correct to use?
I don't understand. It seems you answered your own question.

Some example usage:

去学校 (go to school)，去公司 (go to the office; 去上班 go to work)，去旅行 (go on a vacation)，去法国 (go to france)

出门 (leave the building)，出去 (go out)，出来 (come out)，出国 (leave the country)

回家 (go back home)，回去 (go back)，回国 (go home [from abroad])，回公司 (return to the office)，回学校 (go back to the school)