Úlfarsfell is one place that comes to mind, it's about 10 minute drive from the center: http://maps.google.com/?ll=64.152432,-21.731558&spn=0.032705,0.083427&hnear=Reykjavik,+Iceland&t=h&z=14
http://uni.hi.is/ths124/files/2011/08/800px-%C3%9Alfarsfell.jpg