David Bosco has a theory as to why it's the only international organization the right routinely goes after:

[T]he UN–at least its General Assembly–is a forum in which the United States is routinely outvoted and in which its special place in the international system receives no formal recognition. What's more, many of the states that vote against the U.S. are themselves corrupt and unrepresentative.  The UN General Assembly is quite unique in this respect–it's the one multilateral forum where the U.S. can be humiliated–if losing a public vote should be thought of as humiliating–on a regular basis. Most other institutions, including the World Bank, IMF, WTO, and NATO, either operate by consensus or accord the United States special voting powers. 

He documents the hate among GOP presidential candidates here.

(Chart via Brett Schaefer.)