This is very tough nut to crack. Not only is the apartment an issue, but you also need VHF-high for 3 of your stations. So you need a small 7-51 antenna, like the RCA 751, Winegard 7694, or Antennacraft HBU 22. Rabbit ears and indoor loops aren't gonna cut it with noise margins that low.http://www.tvfool.com/?option=com_wr...03d926ea24c3fa
You didn't say what floor you are on, so I used the default 10 foot height. More height doesn't really help much because of Cougar Mountain being in the way- the farther north you are from Jak's Grill, the better. You would want to tilt the antenna upwards so that it points at the hoizon (the aforementioned Cougar Mountain). If your deck is on the north or east side of the building, that would probably be the best spot. But if the deck doesn't have a view to the northeast, a window that faces north or east might work better than the deck.
A preamplifier is probably a good idea if you have any more than 15 feet of cable from the antenna. You can't afford to lose any signal in the cable.
A diy Gray-Hoverman might work for you, if you have the inclination to build. The G-H does great on VHF-high channels and has a vertical form, which generally is easier to deal with on a balcony or hanging in front of a window.
It should be possible to get everything down to the NBC, but you may have to tee off your landlord to get there.