And while these touches are certainly due in part to European immigrants who flooded Argentina in the wake of both world wars (the melting pot vibe is palpable throughout the country: Middle European efficiency, Parisian style, Italian panache), there’s also an easy homegrown sense of hospitality that is a lifestyle vernacular all its own. Covering distances by car and short flights will let you experience a range of landscapes and game. If you’re just along for the ride, there are plenty of non-hunting and -fishing activities at each stop. My wife, Yolanda, and our daughter, Clara, joined me on this trip. (Turned out the right time to hit my dream trifecta of stag, birds, and trout aligned with my daughter’s Spring Break.) Our spring—fall in Argentina— means far fewer tourists than during South America’s summer, and still-warm weather. Since we had just one week, we enlisted our friend and travel specialist Maita Barrenechea of Mai 10, an Argentine expert on Buenos Aires who is also super-knowledgeable about the best places to hunt and fish throughout the country.

GET YOUR BEARINGS – Start with a couple of days in Buenos Aires. After stumbling off a long flight, the last thing you’ll want to do is catch a domestic flight to Patagonia. We stayed at the Alvear Palace Hotel, a grand French-style palace dating to the 1930s that was recently refreshed without sacrificing any of its original charm. We loved the concierge, who remembered our names after one meeting (and directed us to the best ice-cream joint, Persicco, around the corner), the over-the-top breakfast buffet that had addictive mini-churros, and ending the day at the hotel’s wood-paneled bar, where black-tied barmen serve the perfect high-low combination: spot-on martinis with Pringles.

The hotel is in the tony Recoleta neighborhood (within walking distance of Eva Peron’s tomb in Recoleta Cemetery), home to excellent shopping. (Bring U.S. dollars—American cash cuts the price in half.) Our favorite store was Arandu, a vast four-story emporium of Argentinian craftsmanship that stocks hunting and polo equipment alongside the best edit of alpaca ponchos, leather shoes and belts, canvas espadrilles, and beautiful leather and sterling silver mate bowls with silver straws. A short stroll from the Alvear, the cobblers at Guido have been crafting beautifully cut custom leather loafers for more than 60 years. Get measured and have them shipped home.

You won’t find better shopping the rest of the trip, so even though it’s the start, stock up on souvenirs and gifts. For meals, we mostly chose places that were a short walk from our hotel. For lunch we liked La Biela, a neighborhood sidewalk cafe that’s been around since the 1950s, and went with the local order: a Milanese-style pressed cheese sandwich followed by a Fernet-Branca digestif. For our first Argentinian steak dinner, we headed to Fervor. The vacio del fino (thin flank steak), rare, with a spicy arugula salad, is the way to go.