You could do any of the following...
1) Image gallery where they can upload files and show them online. Let friends view them with special permissions etc.
2) You could do a basic forum which lets users signup, add posts, and have moderators that can edit, move, delete and lock posts.
3) Create a file manager which will let people manipulate files through a web interface. Control file permissions, location of files, add/remove directories etc.
4) A "small" content management system. I say small because this could easily get you into a bigger project than 6 weeks. Perhaps limit it to managing only one file type (like text files), assigning different levels of review, management of the files location and maybe basic editing. (textarea box comes to mind)
5) Bookmark uploader and sharing system. Allow people to upload their favorites/bookmarks to the site and manage them. They can review one another's book marks and add them to their own if they like them. Add/remove bookmark folders for better organization. Extra: Allow the site to generate a new bookmark file from your online favorites which they then download and can use with their browser.
Here are just a handful of ideas. Feel free to mix and match or expand on any of them for a great 6 week project.
Enjoy!