How can I export my iPhone notes to text files, preserving the modification date?
In OS X, they're automatically synced to Mail.app. There is a section on the left side of the screen that says "Notes." If you like, I can post screenshots later (not at my MacBook right now).

Here's a way to sync them with a Google account. This is pretty cool, and probably the best way to sync between multiple computers/ devices. Check it out. If you don't have a Google account, might be worth it now lol.

Hope this helps!