Moved from NYC to NJ in September but working in NYC. On NJ return, how do I fill out the double taxation section?

Let's assume

I worked in NYC the whole year for a total income of $48k
I lived in NYC for the first 8 months then moved to NJ
I only paid NY state taxes and NYC local taxes
I earned 34k while living in NYC (6k is from a job that ended before I moved)
I earned 14k while living in NJ for the last 4 months
I only paid NY taxes on my W2s for the whole year

I completed my part-year resident NY return and now I'm stuck on the "Credit for taxes paid to another state" section. It asks for the "other state information" where I can choose either a state or jurisdiction. What do I choose? NY state or NYC the locality? Does it matter?

Then it asks for the "double taxed income while a resident of NJ" and the "tax paid to NYS" (or NYC if I choose that). I am not certain what to enter here. How do I fill this out? Do I fill out the "tax paid to NY" with the total taxes I paid the whole year to both the state and the locality?

And one more question to make sure I'm covering all my bases. Do I have to fill out just the two returns other than federal - NY and NJ part-year resident tax returns?

Thank you!