You could also quite easily go to Amsterdam Zuid station, which is only 5 minutes from Schiphol by train. You wouldn't see anything particularly 'Amsterdammish', but could wander (or tram) up to the local shops on Beethovenstreet, in the very 20s/30s Nieuw-Zuid area. It's an expensive suburb, and there's some pleasant cafés and restaurants up here (I always used to enjoy Fidelio, on the corner with Stadionweg).