Wife has a conference in NYC in mid Sept, and we're planning on making a weekend of it, sans kids

. It will be the first time in NYC for both of us. Looking for recommendations, transit options, hotel vs hostel vs air bnb type stay, must dos...
Rough plan as of now: conference ends mid day Thursday. Plan is to fly in Thursday (afternoon-ish), and check in to the hotel. No idea yet where conference is being held which I know isn't very helpful but may not be important. Leave either Sunday or Monday depending on Airfare prices. Non uber/cab transit will be new to us. Is there a good website I can begin to familiarize myself?
- We're foodies, wife has seafood allergy but other than that we want to see what the city offers (musts are NY style pizza, and apparently black and white cookies, others?). Don't mind spending some cash, but a $500 meal for 2 isn't how we roll. We're more of the hole in the wall bar, or one off restaurant. Would prefer to steer clear of chains.
- not huge musical/play people, but wouldn't object if it worked out.
- was thinking Statue of Liberty, and maybe time square (maybe not after El Floppo's post).
- MoMA a must? Central Park?
- safety concerns?
Just starting to look into it so any advice is appreciated.