We actually traveled across the bridge to get to our bed and breakfast, so this was much less out of our way than it would be for most people. This is probably a 10-15 minute walk from the center of town. The bridge is likely 150 feet (at least) below the level of the town. Therefore, the walk there won't be too bad, but walking back will make your calves and glutes burn on the steep hills.
The bridge itself is interesting to look at, but there is no explanation on the site of its importance or history. Therefore, you really will be going just to see it. You also have a very nice and different vantage point for seeing the city.
We were in town for two days and I'm glad we took this route on our way back to hotel, but I'm not sure it would be worth the trek if you only had one day in Rothenburg. If you want to see the bridge and have only one day, you might consider driving by it and stopping on your way in or out of the city.
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