We probed the local electronic properties of the mixed-valent Co+4-x triangular lattice in NaxCoO2.yH(2)O by 59Co NMR. We observed two distinct types of Co sites for x > or =1/2, but the valence seems averaged out for x approximately 1/3. Local spin fluctuations exhibit qualitatively the same trend down to approximately 100 K regardless of the carrier concentration x, and hence the nature of the electronic ground state. A canonical Fermi-liquid behavior emerges below approximately 100 K only for x approximately 1/3.