Hiking the Inca Trail or wandering through Machu Picchu is best during the shoulder season. If you head there in May or September, you avoid the heavy rains and the worst of the summer tourist crush. You get clear mountain views and slightly more space to breathe in the high-altitude air.
A trip like this usually runs about $2800. To manage that without paying interest, you can use the Discover it® Cash Back. It offers 0% intro APR for 15 months on purchases and balance transfers, which turns that big cost into manageable monthly payments.
The 15-month intro window is a deadline, not free money. If you have a remaining balance when the 15 months are up, you will start paying interest on whatever you still owe.