Tongariro National Park, in the North Island of New Zealand, is a beautiful, serene place with a volatile history. Home to multiple volcanoes - including an active one that erupted as recently as 2012 - as well as craters and lush greenery, the park was unique enough to be used as the setting for "Mordor" in the Lord of the Rings films.
Fortunately, the Tongariro Alpine Crossing gives you the entire range of scenery in a single 19-kilometer hike. The day hike is moderately strenuous, although I should note that the volcanic rock is particularly hard on the knees and feet. Weather can also change rapidly, so I advise either booking a tour guide that will provide you with gear, or preparing for snow conditions regardless of when you go.
To travel there from the U.S., 75,000 American Airlines or 80,000 United Airlines miles will get you a round-trip economy ticket to Auckland, from which Tongariro is a three-hour drive. 125,000 and 160,000 respectively will book a business-class ticket with fully-flat beds - an excellent option, given the flight duration.