We present a study of Nernst effect in underdoped La(2-x)Sr(x)CuO4 in magnetic fields as high as 28 T. At high fields, a sizable Nernst signal was found to persist in the presence of a field-induced nonmetallic resistivity. By simultaneously measuring resistivity and the Nernst coefficient, we extract the entropy of vortex cores in the vicinity of this field-induced superconductor-insulator transition. Moreover, the temperature dependence of the thermoelectric Hall angle provides strong constraints on the possible origins of the finite Nernst signal above T(c), as recently discovered by Xu et al. [Nature (London) 406, 486 (2000)].