Find a point in the intersection of two regions

{x, y} /. FindInstance[x ^ 2 - y ^ 3 ≤ 2 && x ^ 2 + (y + 2) ^ 2 ≤ 1, {x, y}]

{{0, -1}}

RegionPlot[{x ^ 2 - y ^ 3 ≤ 2, x ^ 2 + (y + 2) ^ 2 ≤ 1}, {x, -3, 3}, {y, -3, 3}, PlotStyle -> Table[Directive[Opacity[.5], Hue[t]], {t, {.3, .7}}], Epilog -> {Red, PointSize[Large], Point[{0, -5 / 4}]}]

-Graphics-