The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in \(W^{2,1}_{p,\mathrm{loc}}\) with \(p\in(1, \infty)\). As a consequence, the smooth-fit property holds.