Note: I found the solution for this already; I'm just posting this as a signpost if anyone else has the same issue. Skip to the bottom for solution.

I've copied our website to my laptop to test some things, but now the K2 images appear to be inaccessible.

I think its because on the original site, it's installed at the root level, but on my local machine I have it installed in a subdirectory.

I've checked and all of the items have the correct ids, and from what I understand the image names are based on the id for the item, so I don't know why they are inaccessible. I can see the images in /mysite/media/k2/items/src so it's not like they're missing.

Solution:

In my case, the issue was that the cache folder was empty, because my site backups exclude the K2 cache because I believed it was redundant. And I was kind of right; it is redundant, but the site won't re-generate those cached images automatically like I assumed it would. You have to do it on your own.

There is a tool online for achieving this. I can't link to it, but google "Rebuild K2 Image Cache" and you should find it.