Yes you can deduct the cost of the classes to earn your teacher certificate as part of the Lifetime Learning Credit for both your federal and New Jersey tax returns.
However, you cannot deduct the hotel and transportation expenses. The IRS has determined travel is not a qualified educational expense.
To enter in Turbo Tax:
Federal
Deductions & Credits
Scroll to Education
Select Expenses and Scholarships (Form 1098-T)
This information will automatically import into your state tax return.
For more information, follow this link: IRS on Education