Cycling is the one of the best way to explore this area, if you have no access to car.
Around Amanohashidate(天橋立) train station, many shops where you can hire bicycles.
Average cost: 400yen/bike(2hrs), then 200yen/hour after the first 2hrs.
In Miyazu area:
・Michi-no-eki Umi-no-Kyoto-Miyazu(道の駅 海の京都 宮津）which is located opposite side of a shopping centre called "Mipple". About 12mins walk(950m) from Miyazu station.
Price: 400yen/bike(2hrs), then 100yen/hour after the first 2hrs.
Or you can rent for a day(need to return until 17:30):1000yen/bike.
Many of inns in Amanohashidate&Miyazu area offers rental bikes for their guests as well.
◆Bicycle drunk driving is illegal in Japan◆
Please take left side of the road. You should follow the direction which car is taking. Although on pavement, you can cycle to both directions.