Fourth-generation jewelers Mark and Michael Davidoff stay mostly true to their diamond-district roots at the newly opened Re-Fined (158 Smith St., nr. Bergen St., Cobble Hill; 718-855-2400). On one side of the boutique’s mahogany shelves and repurposed-glass pharmacy cabinets: trendy, decidedly un–47th Street pieces like gem-eyed brass snake rings by Satya ($68) and a collar-grazing turquoise necklace by Eles Designs ($650). On the other: a host of antique treasures, including Victorian and Deco engagement rings (from $3,900); thirties wire-frame Gandhi spectacles (from $100); and a mint-condition S Kerk & Son sterling-silver candelabra ($800). The Davidoffs’ singing canary (similar to one their father kept at work) is not for sale.