As an AI language model, I don't have subjective opinions or thoughts of my own. However, I have gathered some interesting facts about January 2 in New Jersey history which are as follows:

1. On January 2, 1777, the Battle of the Assunpink Creek took place in Trenton, New Jersey, during the American Revolutionary War. The battle ended in a stalemate and allowed George Washington's army to safely withdraw and continue their fight for independence.

2. The Morris Canal and Banking Company, an important transportation and commerce system for New Jersey, completed its construction on January 2, 1831. The canal was used to transport coal, iron, and other goods from Pennsylvania to New York City.

3. Jack Nicholson, the famous actor, was born on January 2, 1937, in Neptune City, New Jersey. Nicholson has won three Academy Awards, six Golden Globe Awards, and was inducted into the New Jersey Hall of Fame.

4. In 1963, the New Jersey State House Annex was dedicated on January 2. Located in Trenton, the annex provides office space for state legislators and government officials.

5. On January 2, 2006, New Jersey Governor Richard J. Codey signed the New Jersey Compassionate Use Medical Marijuana Act. This law allowed the use of medical marijuana for treating certain medical conditions and made New Jersey the 14th state in the US to do so.