Hotels in city areas are usually surrounded by cafes and other places that offer free wi-fi hotspots. Rooms on higher floors (above traffic light levels) usually can not pick up strong signals, but a good wi-fi detector can find a strong signal from a first or second floor room.
Sometimes an encrypted connection is free for customers, so getting internet access might be as easy as stopping in, buying some coffee-to-go, and asking for an access code. Test out the connection in the lobby or hallway before actually switching rooms.
[Photo credit: Flickr user dana~2, used in accordance with Creative Commons]