Several monuments and sights listed on this page including Durbar Square in Kathmandu & Patan, & buildings circling Swayambhunath (Monkey Temple) were damaged or destroyed during the earthquakes. Although all are currently open (as of late August, 2015) Check the status of these sights before visiting.
Durbar Square: North of the Bagmati River in the heart of old town stands several traditional palaces where kings were once crowned. Many of the palaces have two to three tiered roofs in a Nepali "Pagoda" style. Although some buildings date from the 12th century, many stand from the 17 & 18th centuries and were rebuilt after the devastating earthquake of 1934. You can spend hours wandering the various squares, gazing at the many temples where devotees continue to give offerings to the Gods, and visit the Tribuvan Museum. For the best view of the square climb the stairs of the Maju Deval however the entrance to the stairs may be closed or not accessible to non-Hindu's. "Freak Street", south of the Square where the hippies once roamed in the 60's & 70's has been replaced as a tourist mecca by Thamel. Although still unique and great for cheap often dingy rooms, is a mellow although past its prime tiny corner of Kathmandu to spend a couple of days. Basantapur Square in the southern part of Durbar Square has an assortment of artisan's and merchants selling many exquisite wooden figures and crafts.
Bodhnath Stupa: In the Kathmandu Valley, on the northeast outskirts of Kathmandu stands one of the most serene experience in Nepal outside of the Himalayas. Built in the 6th century AD, destroyed by the Mughal's in the 14th century, and rebuilt in past centuries, Bodhnath is a whitewashed Buddhist stupa and Unesco World Heritage sight and the largest stupa in Asia. Circumnavigate the stupa, spinning prayer wheels while muttering a mantra, visit various shops, and mingle with other pilgrims. The symbolism is rich and plentiful on the stupa grounds and you can stay in various hotels/guest houses and learn more about Buddhism. In chaotic Kathmandu, the grounds surrounding Bodhnath Stupa is a play we could stay for days.
Thamel: Before going to Nepal I heard various negative reports about Thamel, comparing it to Khao San Rd in Bangkok, however Thamel can be quite an enjoyable place if you know where to look and watch out for the motorized vehicles. It's also a great place to get your bearings when first coming to Nepal or after a long trek where all you want is a hot meal and the comforts of home. There are some excellent and authentic restaurants and food vendors in addition to Nepali antique stores, outdoor gear stores, bars/clubs, book stores, and guide companies. There is also your range of hassles, poor food, and hustlers, however we never felt unsafe or hassled like we did in parts of India. Word of Advice: Be wary of hiring a so called "guide" who approaches you on the street offering guide services for super cheap. You get what you pay for and these guys often may not know the trail you are hiking or be unethical in their treatment of you and potential porters. You are also taking business away from some excellent Nepali run companies with hardworking and excellent guides and porters.
You can find recommendations for food, lodging, and guide companies by clicking on the following links:
Food in Kathmandu
Lodging in Kathmandu
Food/Lodging on the Trail
Recommended Guide Companies
Kathmandu Outdoor Markets: The area around Chhetrapati Chowk, Thahiti Tole, & Asan Tole is the setting for several outdoor spice & vegetable vendors, butchers, cloth and electronic merchants, and stalls selling everything you need for modern and religious life. You will find various cloth and spice vendors in Asan Tole where you can find more wholesale and higher quality spices (for lower cost) then more touristy sections of Kathmandu but be ready to bargain.
Swayambhunath: In western Kathmandu, about a 25-30 minute lovely walk from Thamel sits this striking Buddhist Temple & Unesco World Heritage site that you can approach in two ways. The far more enthralling is to climb the hundreds of stairs built in the 17th century or the more direct western route. Once you stand on the pinnacle of the temple you will get a spectacular view of the Katmandu valley. Join pilgrims in circumnavigating below the temple, spinning the many prayer wheels and visit the many food stalls and shops selling various religious items. Swayambhunath is know for the throngs of monkeys scattered throughout the site so please watch your belongings and be careful if have a snack in tow. On top of the temple stand various. Please Note: Many of the buildings, except the Stupa on Swayambhunath were destroyed by the April 25th earthquake.