This small bed-and-breakfast plays up its name: The handful of rooms are named for different species of palm tree, and the inn overlooks Greene Square. That puts this inn on the easternmost edge of the Historic District. It is one of the smallest and most affordable of the B&Bs. The house was built in 1987 and got the renovations that transformed it into a B&B in 1998. Look for atmospheric touches here like claw-foot bathtubs, a generous sprinkling of fireplaces (even in bathrooms), and British Colonial–style furniture. Guests can expect a hot breakfast as well as afternoon refreshments. Some of the rooms are equipped with Jacuzzis.