In this work we deal with a nonlinear Schrdinger equation in dimension N ≥ 3, with a subcritical power-type nonlinearity and a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of ℝ^N, where 1 ≤ k ≤ N - 1, as ε goes to zero. The radius of such sphere is related with the local minimum of a function which takes into account the potential V . Variational methods are used together with the penalization technique in order to overcome the lack of compactness.