(I'm going to cross-post too, but in the future please try to limit posts to a single forum - thanks!)
Well, it depends. As a web user I would have concerns if my IP address is directly linked in any way to both my identity and/or my search terms, and is public. Publicizing search terms or other info in such a way that it can't be linked back to a specific individual is, I think, okay.
Basically, keep your users' privacy in mind. Making public anything that links back to them personally should be considered very carefully.
You might want to think twice before making IP addresses public, too. If you have a community associated with your site and there's any chance someone might get into some sort of argument with someone else, having the IP address of one's "opponent" makes it a lot easier to do all sorts of nasty things to them (denial of service attacks, crack attempts, you name it). From a pure network security standpoint, you might want to consider keeping those IP addresses to yourself.
Just my opinion. :>