Security implications of public nonce
The only requirement posed to the nonce in the "Security Model" paragraph of the crypto_box documentation is uniqueness for each pair of communicating parties. In fact, the documentation explicitly recommends incrementing nonces starting from zero (which an attacker could easily brute-force) or random nonces (which need to be transmitted together with the ciphertext anyway).

Therefore, sending the nonce publicly should be secure (unless some underlying primitive is broken, of course).