I am going to be starting a hobby project with a friend, but we'll need some (free) way to organize and store tasks, bugs, etc. What tool do you recommend to do this? can something stored through an SVN server work? (Offline would be best)
It's not an offline solution but you could getting a JIRA Personal edition license which is free.
It does all the above and it also integrates well with version control such as SVN/GIT (you can link tasks/bugs to commits)
GitHub has an issue tracking system. No need to configure anything, and should be good enough for hobby projects.
I've never used it, but Redmine is available; it may be overkill, though.
Versioned Artifacts stores data in version control. It's free if your project is open-source.
I'll recommend what I use:
http://www.fogcreek.com/FogBugz/StudentAndStartup.html
"The FogBugz Student and Startup Edition allows startups of two people to use a complete, full-featured version of FogBugz, professionally hosted at our data center, at absolutely no cost."