Before you do anything and start shopping for a new TV antenna, my cable-less friend, you'll want to direct yourself over to AntennaWeb.org. From here, you can determine the best antenna type attuned for your location and viewing preferences. Here's an example of our Los Angeles apartment and the reception strength/direction from broadcasters nearby. The map gives me a good idea of where to position an external antenna according to channel:
Small HDTV Antennas
Despite the shape, you should be able to pull in more than 8 channels with this numerically shaped indoor/outdoor Antennas Direct C2 ClearStream Television Antenna from Antennas Direct. Rated for a range of up to 50 miles, the unit is basically a miniaturized version of those huge outdoor antennas we all grew up seeing on rooftops, and was picked as the Wirecutter's best HDTV for city dwellers. Some owners report pulling in 30+ channels with this fairly compact unit. Just note, this unit is primarily for UHF broadcasts.
If you live somewhere with a pretty solid over-the-air broadcast reception this extremely affordable and compact Philips Indoor Amplified Dtv Antenna might be your ticket. One LA resident reviewer claims over 60 channels, but mileage will vary. But there's no argument this is probably the cleanest design for an external antenna unit we're run into, with appearance similar to a center speaker or small soundbar. At just $7.24 over at Amazon, it could be an ideal second bedroom TV antenna.
(Images: top photo Shutterstock; others as linked above)