  Polycrystalline samples of NaYbO$_2$ 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 $^{23}$Na 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-$\frac{1}{2}$ triangular-lattice antiferromagnets
