We consider the problem of finding a saddle point for the convex-concave objective min(x) max(y) f(x) + < Ax, y > - g*(y), where f is a convex function with locally Lipschitz gradient and g is convex and possibly non-smooth. We propose an adaptive version of the Condat-V (u) over tilde algorithm, which alternates between primal gradient steps and dual proximal steps. The method achieves stepsize adaptivity through a simple rule involving ||A|| and the norm of recently computed gradients of f. Under standard assumptions, we prove an O(k(-1)) ergodic convergence rate. Furthermore, when f is also locally strongly convex and A has full row rank we show that our method converges with a linear rate. Numerical experiments are provided for illustrating the practical performance of the algorithm.