CITY OF OAXACA, MexicoTourism to Mexico is a mixed bag, as high-end resorts abut areas of extreme poverty. Throw in recent political tensions around the border and news about drug-related violence, and Americans have many reasons to steer clear. But in addition to being close — and a bargain, thanks to a favorable exchange rate — Mexico offers a gorgeous, varied landscape and an array of fascinating indigenous cultures, especially in southern Oaxaca state. Living here for a year has given my family the chance to do a lot of off-the-beaten path travel. One of our favorite jaunts was a day hike to the petrified waterfalls of Hierve el Agua (named "the water boils" in Spanish, for the mineral-rich springs that "boil up" there, creating the petrified falls). This is the most popular day hike offered by Zapotrek ecotour company, based in the city of Oaxaca and founded in 2014 by Eric Ramirez, an energetic, upbeat guy who speaks English like a Californian.Ramirez grew up in the Zapotec-speaking town of Tlacolula, outside Oaxaca, and crossed the border into the United States with his family when he was only 11. After attending high school in Anaheim, Calif., and waiting tables in Beverly Hills, he moved back to Mexico when he was in his mid-20s. He saw an opening for someone who could bridge the gap between Mexico’s international tourist trade and small, indigenous communities like the one where he grew up. Taking a Zapotrek ecotour is a satisfying alternative to jumping on one of the many commercial bus tours to archaeological sites and natural wonders that depart Oaxaca every day.Ramirez picked us up at our house at 7 a.m. and took us to a roadside restaurant for a traditional breakfast of hot chocolate, fresh-baked breads and delicious egg-and-tortilla dishes made on the wood-fired comal.We toured a mezcal plant next door, where a horse pulled a heavy stone wheel to crush maguey plants that had been roasted in an enormous outdoor pit. We sampled the cooked maguey fibers — surprisingly sweet.Next, we stopped at a small village to pick up our local guide for the hike. (Indigenous "uses and customs" laws make it illegal for outsiders to traverse communal lands unchaperoned, so Zapotrek set this up in advance.) Palm-weaving is the specialty in the town where we started our hike, and our guide picked a few palm fronds along the trail and deftly wove them into a bird for our youngest daughter as we walked up the mountain. He had no trouble ambling along in sandals, pointing out medicinal plants. For my husband, our girls, ages 11, 14 and 16, and I — weekend athletes all — the "intermediate" climb was a hard push. The path took us through woods and lush farmland, across rushing streams and up into a rocky landscape with tall cacti and sweeping views of the valley below. We were relieved to flop down for a snack at the halfway point — tiny "gorilla finger" bananas, oranges and nut bars from the market — near a hidden waterfall in a cave. We had the place to ourselves as we changed into bathing suits and splashed around under the waterfall, to the children’s delight.We hiked for another hour and a half into the clouds, winding around the mountain and taking in different views of the petrified falls — a set of frozen limestone curtains streaming down the face of a cliff. With thunder threatening in the distance, we arrived at Alice’s Restaurant, at the top of the mountain. We sat under a palm-frond roof to eat quesadillas, guacamole and fried steak, just as the rain began to fall.When the rain stopped, we finished our day admiring the falls and swimming in the spring-fed infinity pools on top of the mountain. The water felt cold at first, then wonderful on our aching legs and feet. The other visitors had all gone home as a pink sunset lit up the mountaintops. The pool ends at the cliff’s edge, so it looked like we were swimming into the sky. Riding home in the van after dark, warm and spent, we fell asleep. Ruth Conniff is editor at large for the Progressive magazine.