One really iconic aircraft is the venerable DC3. Not only is it featured in many aviation museums, but there are still airlines flying it, so you can hitch a ride. But I have to admit that my last trip on a DC3 was in the 1970 in the Azores Islands. A surprisingly smooth and comfortable flight, better than you expect from a pre-war design.
This DC3 is on display in Christchurch, New Zealand.