As with any city, you can live on not very much spending money if that's the way you want to play it.
You don't have to "eat out" for every meal - places like Whole Foods at Columbus Circle have an amazing deli with loads of hot and cold food you can take away. I like to picnic in central park in the warmer months but march might be chilly. Obviously the pizza and hot dog places are good too!
For the sights ~
-empire state $34 each
-lady liberty $18
-top of the rock $38 (+15 if you want to do 'sun and stars' visiting twice in a day during daylight, then again after dark)
-broadway show - variable but I usually buy my tickets from TKTS in Times Square the same day. It's quite a bit cheaper and so far I've always been lucky with seats. You can check whats available on their website:
https://www.tdf.org/nyc/81/TKTS-Live
-you'll probably spend a fair bit of time doing stuff that's free as well like seeing central station, brooklyn bridge, times square (find the naked cowboy!), and checking out different areas of Manhattan.
-take a dump in the foyer of Trump Tower $priceless
For travel, you can get a 7 day unlimited metro card for subways/buses for ~$32. If you're going to use public transport more than about 10 times during your 4 day stay, it's the cheapest way to do it vs. buying daily/individual/top-up tickets.
Don't forget about tips as well - food will cost you 20% more than the listed price.
Have you decided where you're staying yet? If Manhattan is proving quite $$$ try Jersey (Newport area). The PATH train runs pretty much 24/7 and takes 15 mins to get to Times Square so you'd get more lux for your money out that way.
Have fun!