"There's a great value going to France now, and the crowds have thinned," explained Judy Stein of Ovation travel, which handles corporate and ultra-VIP travel. "People are going to go to Burgundy because of the passion to go—if they’re serious, serious wine connoisseurs—versus other areas where people are interested in having a wine experience combined with a comfortable property."

During a recent visit, I stayed with friends in a perfectly renovated 17th century stone barn in the Chardonnay-drenched town of Meursault. The property overlooked a small parcel of vineyards and had been painstakingly converted into rental apartments (going for about $2,000 a week). More than a hundred such properties are dotted through the charming villages of the Côte de Beaune and Côte de Nuits.

Wandering up twisted streets among stone walls threaded with blossoming rose vines, it felt like the best way to experience provincial town life. In the morning, you grab a pastry at the boulangerie on the impeccably charming town square, and then a coffee at the restaurant-slash-grocery-slash-bar in which the locals seem to hang out all day. You admire the colorful tile roofs on the teetering town hall, straight out of Beauty and the Beast, taking a moment to relax. Then you wander home, get in the car, and start your day.

There are dozens of comparable towns you could call home base, so when scouring the Internet, look at Pommard, Santenay, Flavigny, Puligny-Montrachet, and Volnay if you want to be among the vines. For a more traditional hotel experience, the wine crew tends to pick L'Hotel de Beaune (rooms start at $427 a night) and Hotel de Cep (rooms start at $396).

What to Do

A bike tour of the Côte de Beaune was my first trek on a visit in June ($40 per person). Our guide was the first of many to try to explain the internecine, archaic way by which wine is classified in the region as we stopped to taste bottles along the way. Even if you think you will never understand it, locals do their best to drill the system into your head.

As we looked down from the hillside in Volnay, we were told about the premier and grand cru vines that grew near the top of the ridge above us, the third-tier "Village" wines grown around us, and the low patches of land that are allowed to generate only what the locals think of as generic plonk (Vins de Bourgogne) down in the flatlands of the valley. To me, even those were quite tasty.

Even without the wine history, a bike ride is a perfect way to explore the hillside: Dozens of tiny, quiet roads trace along the slope and between towns that are each more picturesque than the last. Even if you get caught in the rain (as we did, hiding under a centuries-old roof in the blossom-filled courtyard at Domaine Lahaye) you will have a muddy good time.

A historical tour is also in order, as some of those medieval towns are nearly too cinematically cute to be real. Authentica Tours or Burgundy Discovery Tours offer trips to multiple towns, where well-informed guides will help you cover a lot of terrain in an afternoon or full day. The towns of Semur-en-Auxois, with ancient towers and hilltop town square, and Flavigny-sur-Ozerain—where the movie Chocolat was filmed—are worth an afternoon's wandering.

Be sure to make time for a self-guided tour of the breathtaking Abbey de Fontenay, the historically compelling Cluny Abbey—where a clever 3D digital restoration helps long-lost buildings come alive—and the sumptuous Hospices de Beaune, with their steep, glazed-tile roofs and overly ambitious audio tour.