Is there even a difference between the two?
My thought is that "purpose of" refers to an intended function of an item. "Purpose for" refers to how an item will be used, regardless of that use's relation to the item's intended function.
Hmm. I'm not describing that well. How about this:
The "purpose of" a shoe is protecting your feet. A possible "purpose for" a shoe is to smash bugs.
So "purpose of" describes a property or capacity of a shoe, where "purpose for" describes what might be done with a shoe.
This is an interesting topic. To add to bikeboy389's response: the purpose of something is the reason it exists. The purpose behind something is the reason in the mind of whoever was responsible for it. My intuition is that a purpose for something is more likely to be a use or reason associated with it after the fact, or subject to debate.
Found via Google:
i.e., giving students a purpose/reason to read; and
i.e., an individual/agent (God) has designated a purpose for something. (The purpose of our lives would frame it as inherent rather than designated, I think. *God's purpose of/behind our lives would be ill-formed, but the purpose of God for our lives is OK in the right context.)
(There are also contexts in which you can use the construction purpose to a thing, e.g. He embraced religion in the hope that it would reveal the purpose to our lives. This feels fixed or archaic compared to the other options.)
You'd say a/the cause of something to refer to its cause. Having (just) cause for an action, though, is a different construction: it means you have sufficient grounds/justification to perform that action, esp. in a legal sense: The judge's flawed instructions are cause for an appeal.
On the other hand, I don't think reason works in the same way: e.g. a/the reason for getting up early and a/the reason to get up early are fine, but *reason of getting up early sounds wrong to me. You could also say the reason for/behind the decision. Words behaving similarly to reason: rationale and motivation.
For me, it feels right to use of when purpose is the subject of a sentence or a clause:
And, also for me, it feels right to use for when purpose is the object of the sentence or clause
EDIT: On the other hand, it just occurred to me that it would also be fine to say:
When you use "purpose of", the reader is expecting an abstract rationale. When you use "purpose for", the reader is expecting a more concrete example. Compare:
The abstract idea is "to educate".
Concrete: "get people talking". Saying "purpose of this website is to get people talking" in the last example wouldn't sound quite right, although it would still be grammatically correct.