@madaboutpurple short term airb&b are illegal in Manhattan.
I lived in Manhattan on and off for 2023, my advice would be use the subway and walk, don’t do more than 2 tall buildings (the Summit would be my No 1) if you plan on doing a pedi cab trip in Cenral park book it beforehand (Central park Attractions are good) but you can just walk.
Take the free Staten Island ferry but just turn around and get it straight back again.
Use the riverboats, take the cable car over to Roosevelt Island then the riverboat down towards Brooklyn bridge.
Walk over Brooklyn bridge, I prefer to walk from Dumbo side towards Manhattan for the views, but both ways are good.
Walk the Highline and start or finish at Little Island (better in summer).
You might get some good offers in February they sometimes have Broadway week/ restaurant week sales/discounts.
Check out BA sale, they do good flight and room offers, personally I wouldn’t stay near Times Sq and you won’t spend much time in your hotel.
Gallaghers restaurant do a great lunchtime fixed price special every day (used to be $30 per head) it’s a traditional steak restaurant, but you have to book.
Most places do happy hour, use that time to try cocktails, food and drink is very expensive, you have to tip, check out the menu before you go in anywhere add 20% to all prices, if you can’t afford it don’t go in, don’t think you can scrimp on the tip.
There are some very good FB groups with tips and discounts so it may be worth joining one whilst planning.
Dont try to do too much, you will be exhausted, have a fantastic trip, NYC is brilliant.