Something like Dropbox for local use with a NAS as storage server
Solution 1:
Look at http://owncloud.org - it's basically a open source dropbox solution.
Don't know what NAS you have but most NAS boxes run on linux and you should be able to get some directions at the owncloud forums.
Otherwise i think Unison or rsync would be the best non server solutions in your case.
This links to a blog post describing the very same problem(and an acceptable solution) but for ubuntu. http://www.cerebralmastication.com/2011/04/fast-two-way-sync-in-ubuntu/
Solution 2:
I looked at this some time ago too.
First, I have tried Sparkleshare which is nice for small document-like repo, but has all not-fun features of git (whole history) and not handle big files well.
I end up with Unison which is very nice software, have bi-directional sync of directories (with backups if there are merge conflicts) - works perfectly for large data. Go for it.
EDIT:
Recently I found really good tool: syncthing (recently they changed name to pulse). Has client for most of the platforms and it's pretty flexible in configuration with nice web-gui.
There is also git-annex, I was using it for short time but I stopped as it's required xmpp account to pass messages (recently this was removed so it's not required anymore but I'm staying with syncthing now for a while).