Microwave-infrared double-resonance spectroscopy has been used to probe the solvation environment and its influence on the rotational relaxation of a cyanoacetylene molecule embedded in a superfluid He-4 nanodroplet. The results support a model in which (within any given rotational state) the guest molecules are distributed over a set of spectroscopically inequivalent states which are most likely "particle-in-a-box" states originating from the confinement of the guest molecule within the droplet. Revisitation of previously collected microwave-microwave double-resonance data suggests that transitions between these states occur at a rate which is comparable to the rotational relaxation rate, but not fast enough as to produce motionally narrowed, homogeneous absorption lines. The relative intensities of the rotational lines in the microwave-infrared double-resonance spectra are observed to depend strongly on the average droplet size. In the large droplet limit we can explain the observed pattern by invoking a "strong collision" regime, i.e., one in which the branching ratios of the rotational relaxation do not depend on the initial rotational state. For small droplets we speculate that, because of finite size effects, the density of (surface) states may become discontinuous, producing deviations from the "thermal" behavior of the larger systems.