Hue is probably the best city in Vietnam for cycling. There is less traffic than the other major cities and the people of Hue are in less of a hurry.
Many choose to cycle along the banks of the slow moving Perfume River and over the Truong Tien Bridge and into the 200-year-old Citadel where one can see the entrance to the royal Imperial City and pass by the many aircrafts and tanks from the American War before continuing deeper into the walled city where life carries on in coffee shops, motorbike repair shops, clothes shops and hairdressers.
Once you reach the end of the moat of the Imperial city you can venture further to see the ponds where women wearing conical hats in fishing boats harvest morning glory (water spinach) and snails. There are many garden houses in Hue and it is lovely to slowly cycle by to admire the intrinsic nature of these properties.
More interesting way to discover other charming of Hue ancient capital is to make a cycling trip around the countryside. Spending half/full day on bike by yourself, you will embark to the rural to admire and enjoy interesting scenes and local life.
For those who would like to smell the fresh air and hear nothing but the fluttering of dragonfly wings then the countryside surrounding Hue is the answer. The central parts of Vietnam are known for their lagoons and Hue is no exception. You haven't to go but 5 kilometers east outside the city before you come across rice paddy fields, vegetable and flower farms, each with a separate village at its core.
If you decide to travel west out of Hue you can experience quite the opposite landscape with hilly routes to the temples, pagodas, royal mausoleums, garden houses and if you continue on you will eventually get to the bamboo forest snaking alongside the Perfume River.