Are there any mods which allow me to send a NPC back to their original location (e.g. Piper to her house, Nick Valentine to his office, etc), or send a NPC to my home in Diamond city?

Not that I know of just yet. The GECK will be out soon and I can't imagine this mod wouldn't be on someone's list as it's fairly critical.

Not yet. But there's no doubt there will be a mod that overhauls or adds to the companion system fairly quickly.

No doubt that such a feature will be a thing, or something comparable like http://www.nexusmods.com/skyrim/mods/18045/? where you could set a home in any location for each follower.

As far as I am aware you can just hit cancel and they'll go back to their default homes or at least that's how it is for me, though it might just be were they were last.

That does work, but ONLY if you have not sent them to a different settlement yet. Luckily I never assigned Nick, so when I dismiss him, I just tab/cancel out of the settlement screen and he goes back to his office. Unfortunately for Piper, I sent her to Hangman's Alley once, and it appears to be her perma-home. This was a major development oversight (lazyness), and will surely be corrected shortly after the release of the CK.