Patan, or Lalitpur as it is usually called, is the second-largest city in the valley and lies just across the Bagmati River from Kathmandu. The town is much quieter, and its main sights can be covered in an easy day's walk. It is located just 5km south from Thamel, and you can reach it by bicycle, taxi, bus, tuk-tuk, or foot. The last option is the most appealing, since along the way are many attractions you will cross: Kathmandu’s Durbar Square, colorful temples, and nice local coffee shops. The main attraction of Lalitpur is its Durbar Square; wise planning will allow a very early visit there, because later in the morning, the place crowds up. The square has the major display of Newari woodcarving-architecture in Nepal and includes the Royal Palace and two-tiered brick Jagannarayan Temple; just below the roofs are carvings of very active couples. The Patan Museum is located there as well, but as usual in Nepal, the building is more interesting than its collection.
North of the square is the Golden Temple, a Buddhist monastery watched over by tortoises and the Kumbeshawar, the oldest temple in Patan (1392). South of the square is Mangal Bazaar, an area of narrow streets lined with many of the artisans the town is so proud of.
Four stupas delimit the historical city, and they are called the northern, estern, southern, and western stupas. Finding them is a little tedious: the eastern one is on the very outskirts, the western and the southern are within densely constructed areas (the last is very close to the bus terminal), and the northern one is off the way to Kathmandu, just before a secondary bridge.
Lalitpur has a small zoo in its eastern part, but if you just came back from the Chitwan National Park, you can skip it in favor of Jawalalkhel, a huge Tibetan Refugee Centre just south of the zoo. There you can buy colorful carpets and help in their precarious economy.
On your way back to Kathmandu, give some attention to the Bagmati River. It is shallow and wide and its rocky riverbed and riverside does not invite for a splash or a picnic, but you may spot cremation rites performed by the local Nepali/Hindu population within an adjacent temple in its northern shore. Unless you are Hindu, your participation or even visit to the site is not allowed, hence a camera with a good zoom is recommended.