I have never been to Cuzco, but it guarantees you a major tourist destination. You can spend 7 days hiking the entire inca trail if you want.
I would also consider which country you would want to return to next time, which country intrigues you long term - beyond your 3 month course. Depending on what that is, this trip could be a jumping off for a longer stay in the future. Wherever you go you will make connections and friends, which will make it easier and more fun to go back there in the future.
They say the hardest choice to make is between positives, they should all be great, so you'll do well whatever way you go.
I would also consider which country you would want to return to next time, which country intrigues you long term - beyond your 3 month course. Depending on what that is, this trip could be a jumping off for a longer stay in the future. Wherever you go you will make connections and friends, which will make it easier and more fun to go back there in the future.
They say the hardest choice to make is between positives, they should all be great, so you'll do well whatever way you go.
“Where the danger is, so grows the saving element.” ~ German poet Hoelderlin