Get your terminology right first.
There are talent agencies and casting directors and then there are casting websites where you can get work.
If you want good jobs, you need two things: experience and an agent. The jobs you see posted on a website are what’s left over once the producers and directors have submitted their breakdowns of the roles they need to talent agencies. For real important roles, they almost never go to casting websites, unless they are looking for something that is really difficult to cast.
Now back to you. If you are not getting any response, it could be what you suspect; that the casting website isn’t any good or not legit. It could be their fault.
It could also be your fault that you are not getting a response. Did you ever think about that? Are you trained? What do you have on your résumé? Where did you go to school? What do you have on your reel? What do your headshots look like? How did you fill out your profile on the casting website? Did you utilize all the tools they gave you to be successful?
If something isn’t working for you, you need to be able to analyze the situation and fix it as quickly as possible.
Go have a look at ActingCareerStartUp.com. It really is made to help you.
What I can tell you though is to start here: http://www.actingcareerstartup.com/nycastings.html
Have a look at the teen acting page as well.
Lastly, talent agencies don’t cost you money. They take out 10% of what you earn AFTER you actually do the job and not before.
Good luck in your search!
p.s. Go to school and really learn how to act and once you find a good school, stay there and keep on training. You’ll be glad you did. Then, learn the business and see how things magically start to happen.