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You'll easily tell which way the second floor joists go in your house by removing a light fixture from the first floor ceiling and taking a look. You'll also see the spacing and construction type.
Joists transfer weight to the outside walls, and/or some inner weight bearing member. The closer your dead load is to where it should transfer the weight to, as well as distributing the weight across as many joists as possible, is your goal. If the joists run parallel to the outside wall you've chosen, it's possible that it may be no better than installing the safe in the middle of the floor. Also considering your closet is probably wider than it is deep, you'll have difficulty distributing that weight over more than 3 joists, considering they're probably on 16" centers.
It might be overkill to consider all these factors, but if you plan on putting that weight there for 10 years or more, overkill when it comes to structural integrity isn't a bad thing.
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