I've just noticed that it seems images didn't seem to transfer over properly... that's a shame. Especially if I want to change hosts in the future, that could be really problematic...
Unfortunately it seems the export feature for Ghost only focuses on the database information, not actual files within the websites directory. But fear not, it's still possible to transfer! Sometimes
Images are kept under /content/images. This folder is right beside where the /themes folder is. Basically, if you can get into the server, you just have to copy these files and paste them in your new directory. Unfortunately (again) I'm not sure how you could go about getting to this directory if you're running Ghost off of their servers, but I think you can get access somehow through command line. I'll have to research and post what I find here.
If you're on Openshift, you can get at these files two ways. You can SFTP using Filezilla and get a nice GUI to copy the files, or you can clone the git repository (as Openshift apparently uses Git for hosting everything) and get at the files there!
If you want to upload your images to your new blog, you will have to clone the git repo, place the files, and push the update. Since it primarily uses git, any changes you make using Filezilla will be overwritten.
I should mention, always make complete file backups of your websites. If you're using Openshift, you can use this command in command line to make a "snapshot" archive of your "gear"/website that you can then use to restore if need be (careful, this was 300MB when I tried it, and that was with this very basic blog!)
rhc snapshot save <app-name>
I'm really looking forward to seeing what plugin support Ghost has in the future...