With their large, lush leaves, banana trees bring a tropical vibe to any backyard. But, if you want to enjoy their dramatic display year after year, you’ll need to protect them from cold winters.

Nestled in the ground among dwarf evergreens, blooming sedum and massive clumps of hosta are seven banana plants, the largest towering 14 feet high and holding fruit.

Across the Northeast, environmentalists and enthusiasts are touting the American pawpaw tree. The fruit-bearing tree has ...