Places to Hike in Bhutan ( a few are listed below) :

PARO:

• The Famous Taktsang Hike : Takes around 4-5 hours depending on your walking pace. A bit uphill for half the hiking trail but really really worth the walk/hike,when you see the beautiful Taktsang Monastery,also famously known as the Tiger,s Nest. For More Detail Go to : Taktsang Monastery Hike
• Chumpu Nye : Not many visitors to Bhutan know of this hike. Its one of the most beautiful Whole Day hike that I recommend for anyone traveling to Bhutan. The highlight of this hike is that we hike to an ancient temple which has a statue of Dorje Phamo, the flying Goddess statue. Then there are silent caves and water falls that makes this whole place serene and out of this world. The hike is moderate except for the last leg of the hike where we have to climb up hill but worth every sweat. For More information Read my BLOG on CHUMPU NYE
• The Kilu Nunnery Hike: Its a walk of little over one hour. The Kilu Nunnery over looks the Paro Valley and is one of the oldest nunnery in Bhutan. It is important as it has been a medidation center for many centuries and house the statues of the Guru Rinpoche and Chenrizig (Avalokiteswara). There is optional walk to Kilu Goenpa whereby one can hike to this monastery from the road en route to the Chelela Pass OR one can drive till Chelela Pass and then takea hike to this monastery. The latter hike being more longer than the former hike.
• Zuri Dzong Hike : This old Dzong, an ancient fortress dates back to 1352 and is a hike which gives a spectacular view of the Paro Valley and the Paro International airport. It is a hike which takes about 2 hours starting at the Paro Taa Dzong or the National Museum of Bhutan and ends above a resort above the airport. Hikers enjoy a peaceful time, a rest now and then to soak the view around. There is a cave too believed to have been used by the Buddha to meditate but this is just rumors and we cannot validate this rumor.
• DraKarpo Hike : This hike to is a Cave where the Guru Rimpoche meditated in the 8th Century. This cave is different from the others as the Guru had actually broken the rocks here to make the cave for his meditation. The Bhutanese from all over Bhutan come here and try and do 108 rounds of the cliff that holds this cave. one round of this entire cliff takes about an hour.

THIMPHU

• Lungtsutse Hike: Its takes around 4-5 hours round trip depending on your walking pace. Its a lovely temple situated above the Dochula Stupas. The hike starts from the Dochula Parking Area. The Hike trail is a very comfortable one with very gradual ascend to the Temple. Upon reaching the temple,you will view the spectacular Himalayan Range of Mountains,and the low lying valleys of Punakha and Wangdue. You have to drive up to the beautiful Dochula Pass and then the hike starts from here.
• Tango and Cheri Hike-THIMPHU: This is a hike in Thimphu and is a whole one day hike. Most monks and Gurus meditate in these Monasteries. Tango is a Buddhist Institute where monks,scholars and high lama graduate with a Degree in Buddhist Studies.
• Phajoding Hike-THIMPHU: This is a hike in Thimphu and is a whole one day hike to the serene temples above the Capital city Thimphu. When you take the Druk Path Trek ,this trek ends its route via Phajoding.  
• WangdiTse Monastery Hike: This temple overlooks the entire Thimphu Valley. Its a pleasant 3 hours round trip hike of a leisure walk on an almost. straight elevation 
• Buddha Dordenma to Changgangkha Lhakhang Day Hike : This is a leisure walk from the site of the Big Buddha and ends at the Changgangkha temple which is the oldest temple in the Thimphu Valley and the place of visit by everyone born in Thimphu as it holds the place of the local deity who is said to protect all born in this valley. Its about 2 hours walk one way at a leisure and slow pace enjoying the valley view and the lush and heavy forest cover.
• Pumola Hike: This hike is a mix of moderate and a bit tough hike. The hike begins at Motithang and its initially uphill abit tough route trying to scale the steep forest. There after we reach a meadow and from here its again some uphill climb until we reach the ridge of the Pumola pass and then finally walking this ridge we will reach the Pumola temple. The highlight of this hike is the really tall swing which is an exciting activity to indulge in,well deserved after an arduous hike.
• TRANS Bhutan Trail – The Thimphu Part: We can do a part of this trail in Thimphu. Starting at the Simtokha road head, we continue through the forests heading towards the Dochula Pass and end the hike at Dochula. Its a lovely leisure walk but without a Guide one could get lost like I did when I took this hike, and came out somewhere in the middle of the hike searching for the road head as it started getting dark. But now I know it well and will not lose my way.

Remote HAA Valley : Haa is the shortest name of a place in Bhutan and is one of the last regions to be open for tourism. There are several places for day hikes as we have many temples perched on high rocks and cliffs.

PUNAKHA:

• Khamsum Yuley Temple Hike: This temple was made by Bhutan’s Queen Mother for the present Fifth King of Bhutan,for his long life and good health. This temple hike will take half a day and is beautifully perched on a hill top. The architecture is fully Bhutanese and only Bhutanese Artisans have worked their magic on this uniquely beautiful temple.

TRONGSA:

• Rukubji Hike: Rukubji Hike/walk is a beautiful walk through the remote Rukubji Village.

BUMTHANG: 

• The Drapham Dzong Hike. This is an ancient Historical and Archaeological Site in Bhutan dating back between 1550 to 1700 century. Just about 5 years back this site was discovered by accident by some villagers.