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Situated in one of the most attractive areas of downtown, between the lake and the square, this apartment-style hotel has a lot going for it. Designer Einar Geir Ingvarsson restored this landmark 1900 brick apartment building, formerly home to the city’s Public Reading Society, with all sorts of cool Scandinavian accents like designer lamps and armchairs and various 20th-century modernist furnishings. Each oversized unit has a unique layout and set of amenities, ranging from terrace access to sofabeds to dining areas. Downstairs are an artisanal grocer and a hip bar with a long list of gin and tonics; plus, instead of a ho-hum on-site breakfast, guests are given a voucher for one at the excellent Bergsson Mathús next door.