Girona is a safe city. Myself I haven't had any problem with the car, but once a customer got robbed. As once in 10 years is a low rate, you may take the risk, just don't leave anything visible in the car.
If for any reason you prefer paying for a secure parking, here are the options:
Parking Eiximenis is the closest to the appartment, but doesn't open 24h a day.
Parking Plaça Catalunya open 24h a day and it's about 10 minutes walk.
Have a look at my map with their location.
