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I suggest you take a look at this, try to understand yourself, in case you have not read this already. If you have furthur questions feel free to ask. Wikipedia is an excellent source btw, for these basic questions.
Magnetic field outside a long solenoid can never be zero. Because a solenoid of finite length will have edges and field will come out. However, if we imagine a straigth solenoid of infonite length or a toroid, it will not have edges from where lines of force can come out. therefore field would be zero outside a toroid or a strigth solenoid of infilite length.
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