The Chicago Manual of Style, fifteenth edition (2003) offers this reasonably straightforward style advice under the general category "Parentheses":
6.103 With other punctuation. ... A question mark, an exclamation point, and closing quotation marks precede a closing parenthesis if they belong to the parenthetical matter; they follow it if they belong to the surrounding sentence. A period precedes the closing parenthesis if the entire sentence is in parentheses; otherwise it follows.
This simple pair of rules endorses putting the exclamation mark inside the closing parenthesis (since the exclamation in question is the parenthetical "no matter how silly!") and putting a period outside the closing parenthesis (since the sentence as a whole is not end-punctuated by the parenthetical exclamation mark). Thus Chicago appears to approve of this form:
Honor your creativity and write down anything that comes to mind (no matter how silly!).
If you aren't a fan of punctuation overload at the end of a sentence, you have at least two convenient alternatives that avoid the "!)." ending here. One is an appealing choice if you don't feel that the exclamation point is crucial to the point you're trying to make. In that case, you can simply drop the exclamation point altogether:
Honor your creativity and write down anything that comes to mind (no matter how silly).
On the other hand, if you don't want to lose the excitement of the exclamation point, you can take the parenthetical expression out of parentheses and set it off instead with an em-dash:
Honor your creativity and write down anything that comes to mind—no matter how silly!
Either way, you avoid a pileup of exclamation point/closing parenthesis/period at the end of the sentence, if such a pileup is something you'd just as soon not have.
As usual with style questions involving punctuation, the Chicago approach is just one of many possible approaches. If you're free to pick your own style, go with one that suits your own preferences; if you have to follow a house or school style, find out what it is and stick with it.