State tax filing

My first guess is that the entries are wrong because I don't have all the information needed. A few things to note regarding NY and NJ income and the differences in taxation. This will help you get started but you may want to look through the links for any extra oddities that could apply to you.

For NY income: 

My guess is the full amount is taxable if you worked in the city all year. Part year IT-203-I (Instructions) state: 

If you were a resident of New York State for only part of the tax year, you must pay New York State tax on all income you received while you were a resident of the state and on income you received from New York State sources while you were a nonresident.

For nonresidents, New York source income is the sum (with adjustments for special accruals) of income, gain, loss, and deduction from:

• real or tangible personal property located in New York State (including certain gains or losses from the sale or exchange of an interest in an entity that owns real property in New York State or owns shares of stock in a cooperative housing corporation where the cooperative units relating to the shares are located in New York);
• services performed in New York State;
• a business, trade, profession, or occupation carried on in New York State whether or not as an employee (see TSB-M-10(9)I, Income Received by a Nonresident Related to a Business, Trade, Profession, or Occupation Previously Carried on Within New York State); and
• a New York S corporation in which you are a shareholder (including installment income from an IRC § 453 transaction).

For NJ income: 

You will file the NJ-1040 since NJ makes you choose between resident and nonresident. NJ also taxes money that was set aside pretax in retirement plans so adjustments must be made. You did not mention box 12 above so I don't know if adjustments must be made on that or other potential income.

Resident Income Tax Return Instructions states:

You must prorate exemptions, deductions, credits, and the pension/retirement and other retirement income exclusions based on the number of months you were a New Jersey resident. For this calculation, 15 days or more is considered a month. If you received income from a New Jersey source while you were a nonresident, you must also file a New Jersey nonresident return. For more information, see GIT-6, Part-Year Residents and Nonresident

To complete return:

You need to complete the NY return before NJ since NJ will give you a credit for the double taxed income. The program needs to know the  amount of double tax income and the liability. You get credit for the lower state tax on the lowest taxable amount.

• Each state calculates taxable income differently. 
• Each state has its own tax rate/ system.
• You get the lowest of both categories as a tax credit.