We describe a system for interrogating the acoustic properties of sub-nanoliter liquid samples within an open microfluidics platform. Sessile droplets were deposited onto integrated optomechanical sensors, which possess ambient-medium-noise-limited sensitivity and can thus passively sense the thermally driven acoustic spectrum of the droplets. The droplet acoustic breathing modes manifest as resonant features in the thermomechanical noise spectrum of the sensor, in some cases hybridized with the sensor's own vibrational modes. Excellent agreement is found between experimental observations and theoretical predictions, over the entire ~ 0 - 40 MHz operating range of our sensors. With suitable control over droplet size and morphology, this technique has the potential for precision acoustic sensing of small-volume biological and chemical samples.