There’s nary a hotel for the budget traveler that beats The Jane. In contrast to the various luxury hotels in the area, the renovated, stylish Jane advertises itself as an “upscale hostel”: close to innumerable clubs and galleries, views of the Hudson, and a centennial-long history of accommodating seafarers. But no worries: By now, the rooms come with modern touches like an iPhone dock, flat-screen TV, and air conditioning. Couples need to book the larger Captain’s Cabins; the standard rooms are, although cozy, just too small for two.