
One can rent bicycles at one of the many bicycle rental shops around Amanohashidate and cross the land-bridge, bike around to various surrounding local tourist spots., etc...
Swim on the sandbar in the summertime while eating dried squid.
The only thing to see in Amanohashidate is, well, Amanohashidate itself. The canonical way to view the bridge is to turn your back to it, then bend over and look at it upside down from between your legs — this is supposed to make the bridge appear as if it floats to heaven.
Direct Hashidate (はしだて) limited expresses run four times a day and connect Fukuchiyama (福知山) or Nishi-Maizuru (西舞鶴) to the Kita-Kinki Tango Miyafuku Line (北近畿タンゴ宮福線); you can manage the trip with local trains for as little as ¥2200, but this will take over three hours and require several transfers.
Dried seafood.
Seafood.
There are some local wineries.