With the experience of the two places that I discovered during my trip to Hué, I recommend that you leave the town behind and make the most of the surrounding countryside which is not well known but is worth the detour. This article is all about getting away from the bustle of the town and taking to time to enjoy genuine places!
The Bach Ma national park is just wonderful! I've been there several times because there is just so much to see. It's about 40 km from Hué, south on National Route 1 and then signposted. You can go there by motorbike, taxi or using an agency, but there is no bus that goes to the park. Once you get there you have to pay to get in and also for a car (if you don't have one) so you can get to the summit. Don't try to walk up, you'll be exhausted before you've seen anything. Once you are at the top the view is magnificent if you are lucky enough to be there on a clear day! Then, go down a bit and you will find the walks. You always feel alone in this park, and hardly ever meet anyone because it is enormous. Don't forget to bring a picnic because there are few places to eat in the park. If you want to get away from the city and reconnect with nature this very real place is made for you! Bach Ma has tropical forest, walks, majestic waterfalls and the chance to see large numbers of birds (350 species). The paths aren't always particularly well-maintained but that only adds to the feeling of adventure!
15 km from Hué and 7 km south east of Thuan An is a paradisaical beach. But be careful if you are going to go as far as possible along the coast, to avoid the "Vietnamese" beach which is dirty and a real tourist trap. Phu An, is a tiny village with friendly inhabitants and an enormous beach with white sand and clear sea... There are lots of fishermen, whose pirogues punctuate the view. If you go to see them they will sell you their catch on the beach... Really delicious! You can sleep in small bungalows or villas (you can choose according to the comfort you want and the price). There's a bar which serves delicious smoothies and succulent seafood. The village plays volleyball and, if you want to, you can play with the Vietnamese while on holidays in Vietnam!
I recommend you spend 4 or 5 days at Hué so that you can visit all these places - you won't be disappointed.