On the edge of the Financial District, the Harborside Inn, a former warehouse built in 1858, is a great deal, and the Greenway and Faneuil Hall Marketplace are right across the street. Every unit has a unique layout and a pillow-top bed, with sleek custom teak furnishings and nautical-themed art. The only tough decision here is whether to ask for a room that faces the street (noisier) or the eight-story atrium; if you’re a really light sleeper, a handful of “cabin” rooms have no windows at all.