Unless you live out in the boonies, you can pick up the local HD channels OTA (over the air) with an antenna. It's compressed less than cable/fiber/satellite, so the picture quality will actually be better. Most HDTVs have an OTA tuner built-in. Use these two websites to determine how many channels are within range of your home, and which direction you'd need to point the antenna.
http://www.antennaweb.org/
http://www.antennapoint.com/
The best small/cheap antenna is the bowtie type. It's rather ugly and bulky though, so is best if you can shove it in a closet or your attic (take note that a longer cable from the antenna to your tuner will degrade the signal and may cause you to lose channels).
http://www.amazon.com/Eagle-Aspen-EASDTV2BUHF-Directv-A...
For a cleaner installation, the flat leaf antennas are nearly as good.
http://www.amazon.com/AmazonBasics-Ultra-Thin-Indoor-An...