My fear for thunderstorms causes me to stay indoors many rainy nights.
My fear of thunderstorms causes me to stay indoors many rainy nights.
My fear for thunderstorms causes me to stay indoors many rainy nights.
My fear of thunderstorms causes me to stay indoors many rainy nights.
The idiom "fear of X" means that someone perceives X as a danger or threat and thus regards it with fear (which is appropriate here). The idiom "fear for X" means someone perceives X as vulnerable, as threatened by some external danger. This is a posture of protective concern for X, very different from being afraid of X.