I'm getting some inquiries for link exchanges but where on XF am I suppose to place their links? Are these links suppose to be visible to the public or are they just 'hidden' somewhere on my site?
They should be publicly visible - so that both people and search engines can see the links.
You could add a "page" node with the links in - but if you intend to add a lot of them, you could consider using a link directory where you can add lots of links into different categories of your own making. There's an add-on available if you want a directory:
I have that add-on but it never occurred to me to use the directory to place other people's links because that directly requires for a bit more info than just a link and a website name.
I do have a few xenporta boxes available for storing html but I don't know where I would place it. Don't want to have it glaring on the front page. Where's the best place to put it?