How much to do you want to spend to put your car in a garage? Let's start with that?
Second, if you park in a garage, do you want to go shopping in between performances, return to your car and put the bags in the car and then go off to Radio City Music Hall? If you're in a garage, that's a bit unrealistic unless you park the car yourself. Even then, if you return to your car which you parked yourself, place bags in the trunk, and then leave, you could be setting yourself up for a robbery. I've seen this kind of thing happen to people who park in garages in suburban malls so why would it not happen in the city?
Unless your teenage daughter goes off by herself while sporting low rise jeans with a tatoo on top of rear end which acts as a bull's eye to men, I wouldn't worry too much about her not being safe. She'll be with you and the theatre area is well-lit and very crowded.
It sounds like you both will have a wonderful time.