I spent two months in Nepal, and good amount of that time was in the Kathmandu Valley volunteering in the town of Pharping and exploring the Valley outside the of the city. Kathmandu itself just oozes history and although it suffers from some serious air pollution, which leaves buildings and vibes a bit grimy at times, it's also easy to overlook that side since it holds so many historic sites. Although the earthquake damaged some of the main historic sites, they are not gone and the fact that most still stand is a testament to the city's long and rich timeline. 

If you're staying in the Thamel area of the city, know that there's a lot more to the city than just that, and you should explore not just the main sites and things to do in Kathmandu, which are spread across the city, but also the neighborhoods around these other sites—that's where you'll find so many other locals and restaurants and aspects that have made Kathmandu the historic city it is. 

My favorite of the key sites include:

• Boudhanath Stupa (of course, this is a key site and truly beautiful to visit and walk around the circle around it, just as the local pilgrims do when they visit). 
• Hanuman Dhoka (Durbar Square)
• The home and story of the Kumari Ghar
• Swayambhunath (Monkey Temple)
• Pashupatinath Temple

Beyond those things, the next best thing you can do is leave the city and go to the villages, the homestays and such that dot the Kathmandu Valley.