Check out a neighborhood called de Jordaan near the city center. That neighborhood has some of the coolest beer-centric taverns (or bruin caves) in Europe. Just walk around there and stumble into whatever bar you fancy. Many permit tobacco smoking, too, though it is technically prohibited.
I was in Amsterdam last summer with a couple of friends and we rented an apartment close to the Jordaan area. I really liked it there, nice pubs and great beer. Should definitely try it out.