mi primera estancia en casablanca comenzo en 1987. Acababa de terminar el instituto y era el viaje de fin de curso. ( esta es la correcta, pero ten cuidado en esto "Acababa de terminar el instituto" did you build the institute? lo mejor seria que dijeras "acababa de terminar MIS ESTUDIOS en el instituto" ) saludos!!

In the first sentence, the verb "acababa" means that you just finished the high school by that moment, so it's like you're saying that in 1987. In the second one, the verb "había acabado" means that you just finished the school by 1987 but you're telling it in another moment like 2012 or other one. However, the first sentence is normally used like if it had the meaning of the second one, so they're correct. I think that there's no such difference.

There are lots of instances in Spanish where you have two words to say the same thing, as in this instance. Consider: ¿Qué haces? OR ¿Qué estás haciendo? Estaba comiendo OR Comía. There are various ways to say things, just as in English. E.g. 'my first stay in Casablanca was in 1987. It was after finishing in the institute and it was the end of course trip.' Or 'my first stay in Casablanca was in 1987. I had finished in the institute and it was the end of course trip' . I agree that 'Acababa de terminar <--> Habia acabado' in this case, but not that 'era <--> habia ido'. Ido is the past participle of 'ir' which is unrelated to 'ser'.