Punta Arena is the sandspit where the lighthouse is located.  It's a nice place to go for a walk and do some beachcombing.  To reach it, there are a few different dirt roads leading towards it.  Park  when you get near, then head out for a leisurely stroll.

There is a significant drop off at the end of the spit, where the water gets pretty deep.  Sometimes you can get nice bass and other fish by casting right off the shore there.  The water is shallow on either side, so for fishing try right off the end of the sand spit.