A neutral idiom with the same basic meaning of "For your information"
Is there a more neutral way of saying "for your information"? As far as I know, it is often used to express impatience, or to be assertive that someone is wrong about something.
Solution 1:
Here is a good sentence which includes the word information but does not need the possibly prickly for your:
Here's some information you might find useful [or interesting, or surprising, or helpful, or of value].
Or you could say,
Tell me if this information sounds helpful or useful to you.
Or you could say,
Here is some information you may or may not be familiar with. Tell me how it sounds to you.