Hi soojin ~

I'm sure I'm in the minority here, but I confine my use of "may" and "might" to distinct meanings (and, I must add, similarly regarding the third of this triad, "can"):

can - has the ability to
may - has permission to
might - the possibility of

As to the phrase it may/might be a good idea, I believe that the meaning intended is it is possibly a good idea, and thus I would use "might."

So ~

I can go = I am capable of going
I may go = I have permission to go
I might go = it is possible (but not sure) that I will go