The NY Times and other media of quality (WSJ, Washington Post et al.) do their best to be accurate. [After the NYT infamously captioned the picture of a bloodied young man as an Arab, when in fact he was a Jew, they retracted it and even interviewed the man in question.]
HOWEVER …. bias is a lot more subtle than that. It’s all a matter of a what stories the press chooses to print; who they interviw, what the headline says, and what pictures get printed alongside the story. To protray Israel in a bad light, the liberal media focuses on what they consider to be Israel’s misdeeds, and ignore the good things that Israel does. Conversely, they emphasize whatever good they can find in the Arab world, and play down the evil.
Thus, it is not necessary to lie. The best propaganda sticks to the truth, but selects which truths to tell.
I highly recommend the website honestreporting.com (established by Aish HaTorah) for some really eye-opening insight into media bias against Israel.