Steak, Steak and more Steak. Can start a thread just on steak joints. Try and find spots to eat all over (China Town,, Harlem, Fulton Fish Market, Brooklyn: Peter Luga's, and don't neglect the delis). Also the weather should be great so stroll in Central Park, and Battery Park. If you got a car try City Island in the Bronx. The village for jazz clubs.
Dinner cruise around Manhattan, China Town, Time Square, Downtown (Fulton Fish Market, Wall St area), Bradley Park. Get discount tix to a play (any play), Wednesday is discount day on Broadway). Should be a lot of outdoor musicians, shows and other sidewalk stuff going on. Of course you got museums for rainy days.
Its hard to tell you what to do, and the hot spots to hit, because whatever you do won't be a mistake.
Also check out the websites of activities going on during your stay there. The subway can be your best friend, getting around, no need for taxis, or even Uber.
I will say that you don't have to go broke enjoying the City, Sometimes you can sit in a spot for a couple of hours and see more than you would in a week out in California. I'll put some headphones on and just chill lookin at the pretty ladies.
Spring and Summer is a great time to 'experience' the City. Whatever you do always be street smart in NYC, in addition to 'tourist smart'
