Polycrystalline samples of NaYbO2 are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range magnetic order are found down to 0.3 K, evidencing a highly frustrated spin-liquid-like ground state in zero field. Above 2 T, signatures of magnetic order are observed in thermodynamic measurements, suggesting the possibility of a field-induced quantum phase transition. The Na23 NMR relaxation rates reveal the absence of magnetic order and persistent fluctuations down to 0.3 K at very low fields and confirm the bulk magnetic order above 2 T. The H-T phase diagram is obtained and discussed along with the existing theoretical concepts for layered spin-12 triangular-lattice antiferromagnets.