Shwedagon Paya is on pretty much the only hill in the Yangon area. It's also the most spectacular Buddhist site in the city, with a huge chedi (or "zedi," as I think they call them here) and dozens of smaller shrines surrounding it. There are many, many Buddha images, many people praying, and many people (Burmese, not westerners) just hanging out. Like Thai temples, you have to take your shoes off to enter. Unlike Thai temples, you must also remove your socks.
The pagoda you see here has the life story of the Buddha in pictures.