Q:

What is the justification for curfew laws?

It's Halloween, and some municipalities are creating curfew laws intended to prevent people under 18 from being in public during the late night hours, for example South Brunswick, NJ.
It seems like this apparently common sort of ordinance could be considered unconstitutional on multiple grounds, in that it is restricting free movement as well as targeting only a specific demographic.
Here is the actual text of one such ordinance.
So here are my questions:

Are this and similar ordinances constitutionally valid?
What defenses could a government make if challenged? Further, based on precedent, would they likely be successful?

A:

1. Are this and similar ordinances constitutionally valid?

Yes.
Some future court might decide the law is invalid at some future time. But that possibility is hypothetical and speculative. Therefore, as of now, the law is valid unless and until it is challenged and overturned.

2. What defenses could a government make if challenged?

It depends on what grounds the law is challenged.
Your question about possible defenses is highly dependent on the nature of any challenge — which you have not specified in your question. The U.S. Constitution, for example, prohibits laws respecting a number of things such as freedom of the press, speech, religion, peaceful assembly, bearing arms, etc. to list just a few of the most notable ones.
But your question does not assert the law in question violates any specific or particular prohibition against it. Although the question mentions "restricting free movement as well as targeting only a specific demographic," it does not specify any part of any constitution that prohibits these things. Therefore, your question is unclear as to what might present a constitutional problem for the law. 
It is also unclear which constitution you think might contain prohibitive language. Is it a federal constitutional issue that concerns you? Or is it a state constitutional matter? In either case, which issue specifically concerns you? Your question needs to address these specifics in order to analyze it and respond in a meaningful way.
Look at it like this... just as it is impossible to prove a negative, so  is it impossible for anyone to conclude with absolute certainty that any law is not unconstitutional because no one can predict with certainty every possible future challenge a law might face. There are just too many possibilities to (pre-emptively) exhaust them all with certainty. Also, no one can predict with certainty how any future court might rule on the future challenges (which themselves are unpredictable as previously argued). Therefore, one can only say I think the law is unconstitutional and here are my reasons. Then others can analyze the law and the reasons; then offer an opinion.

Further, based on precedent, would they likely be successful?

See above answer to question numbered 2.
Laws aren't required to be "justified" by the constitution.
Constitutional justification for a law is a meaningless phrase. There is no requirement for a law to be "justified" by any constitution other than that the legislature is empowered by the constitution to make laws. That's all the justification any law needs. Beyond that, however, no law can violate the constitution as determined by a Supreme Court (or the last court to rule) if challenged.

