I'm not sure you can store a
hidden information on the NFC tag. If that's possible, programming the tag is probably not as easy as it sounds and a bad guy might someday want to inspect it and find the hidden container. I'd personally not do that.
One thing you can do is write an encrypted seed on it. As long as you have a strong password, you can pretty much safely store it around the house. According to
an earlier reply from o_e_l_e_o, you'd need 39 random characters from the full ASCII set in order to have an encryption key as secure as the seed is.
Interesting. I'd say that an encrypted seed may be all I need to secure my Bitcoin on an NFC tag. The real issue here would be "legacy" BTC addresses with public and private keypairs. But I think going the BIP38 route, would achieve nearly the same thing as BIP39 on a mnemonic/seed (if I'm not mistaken). All of this is great, but I'd be nice if I could somehow hide the private key on an NFC tag. It's possible to lock and even set a password on the tag for further security. Something similar to steganography on an NFC tag, would work like a charm. For instance, I could place some "dummy" text that would contain the private key "hidden" underneath.
As far as mobile wallets go, I don't think they'll be able to "read" the encrypted seed or private key from an NFC tag "on the fly". I'm talking about any mobile wallet with the capability of asking the user for the passphrase or password to "unlock" the encrypted private key or seed. Right now, NFC tags have very limited data capacity which greatly limits our options to store lots of crypto keys on a single tag. But if technology continues to evolve and people continue to use NFC, it might be possible to do this someday.