You are correct.  You will be required to file a nonresident NY return.  Your income is taxed in New York because you work there.  Although your wife's NJ income is not taxed in New York, it is factored in.  New York calculates what your tax would be if all of your income were taxed in New York, and then assesses the tax based proportionately on the percentage of your total income earned in New York.  

For example, if you earned 60K in New York, and your wife 40K in New Jersey, New York will first find out how much tax you would pay filing a joint return on 100K, and then charge 60% of that tax (the amount you actually earned there).  Unless you earned very little income in New York, you will pay taxes there and will not give back all of the NY taxes withheld from your paycheck.

New Jersey, as your resident state, also taxes the same income.  However, New Jersey will give you a credit for the tax you must pay to New York on the same income you earn there.  In addition, you will come across a question on the New Jersey return that asks about double-taxed income.  This is the NY income you earned.  You will put that amount in the box so that your credits and income are correctly calculated.

You will want to prepare the New York nonresident return first so that the tax credits may be calculated correctly.  Here is an FAQ to assist you with this:  https://ttlc.intuit.com/replies/3302052

In this case, would you recommend file separately instead of co-filing?

In this case, would you recommend file separately?

No. i would suggest filing jointly.  Turbo Tax makes it easy for you to determine income allocations for both states. 

What if the wife has no NY income, and they filed MFS for federal, and he alone files NYS as MFS. She then only files in NJ.

Just to clarify, does your wife live in NJ, then yes, she would file a NJ return for her NJ income. He would file a NJ tax return for the fact that he lives in NJ but he would would also file a NY nonresident return for the income he earned in NY and take that as a credit on his NJ resident return to avoid double taxation on both NY and NJ taxing him on the same income.