Boston’s engagement-ring scene is as diverse as the city itself, from heritage jewelers and diamond specialists in the historic Jewelers Building to independent designers tucked into the South End and luxury boutiques along Newbury Street. Whether you’re searching for a classic natural diamond, a lab-grown stone, an antique ring or a completely bespoke design, Boston offers plenty of ways to make the experience your own. Knowing where to shop—and what to expect in terms of pricing, customization and service—can make it much easier to narrow down the right ring. Where to Shop for an Engagement Ring in Boston Downtown Crossing & the Jewelers Building. The area around Washington Street and…