My girlfriend lives in a concrete box apartment on the north side of Seattle. Her apartment is on the north side of the building and the few windows she has face west. She has an antenna - simple rabbit ears with a UHF loop - sitting on top of her entertainment center. Its in her living room, basically in dead center for the apartment. Most of the television towers in Seattle are located on the top of Queen Anne, which is southwest from where she lives. Some stations broadcast from Bellevue (to the east) and Tacoma to the south. Her reception is poor at best, although she can get most of the programs she wants without too much difficulty.
Its clear that being in the center of a concrete building is bad. I'm also pretty certain that outdoor antennas are frowned upon.
My question is, how can we maximize antenna reception in her apartment? Cold winters so leaving a window slightly propped open is not an option. Drilling holes is not an option. The ledge on her bedroom window is short, ~4 inches. I was thinking of putting a coaxial extender on her antenna but does that mean I also have to put an amplifier to prevent the signal from degenerating? Cost is an issue in this case.
Here's a diagram of the apartment for reference: