I bought a $15 RCA antenna which mostly works pretty fine in here in NYC. CBS gets some slight artifacts sometimes, just enough to be slightly annoying. I don't get ABC or PBS clearly...FOX is perfect and NBC is mostly fine too.
My question is if I bought a more expensive antenna, like a $40 one, would that make a major difference? Clear signal and more channels all the time?
Your best bet would be to go to http://www.antennaweb.org/ , enter your zip code, and find out what stations are available in your area as well as the location, distance, and direction of each broadcast station. Which antenna you get will be determined by what channels you want to receive. Multi-directional antennae have a shorter range, but 360 degree coverage. Directional antennae have a longer range, but only in one general direction.
NY is not good for HD. The best antenna I have found is the Terk TV55. It works well on Long Island and Queens. It is big and needs to be oriented correctly. Buy one but make sure you can return it if it doesn't work for you.