Where to store my propane torch?
The simple answer is that propane cylinders should be stored outside. That's what every guide will tell you. You really shouldn't even be storing it in a garage. Your yard is the best place, and if you take the safety guidelines seriously, you probably shouldn't own a propane torch if you don't have an "outside" (i.e. you live in an apartment). Either that or you should dispose of the fuel immediately and only store the head.

There's always a risk associated with storing any pressurized gas in your home, whether it's a propane cylinder or a nitrous oxide charger that you use with a whipper. The autoignition temperature of propane is 470° C, about the same as wood and far greater than paper, so it's not just going to spontaneously combust - it needs a spark or a heat source like a burner - so don't store it on your stovetop. The real worry isn't a sudden explosion in the middle of the night but rather a gradual leak, which you can't see or hear, and don't become aware of until it's too late.

Much like most of our food-safety questions, the risks are very small and many folks choose to ignore them - but there is a risk of a fire or explosion. If you intend to store it in your house, you might want to check to make sure it's not specifically prohibited by your insurance policy, homeowner's association, etc., depending on where you live.

N.B. If you do decide to store it in your house anyway, at least keep it away from children, pets, and anything flammable. For example, in a metal toolbox on a top shelf.