People’s Park is very close to the Shwedagon Pagoda. It’s a good idea to visit it after the temple. It is adjacent to the West entrance of the Pagoda. However, usually you will enter the Pagoda by the South Entrance, and as you have to leave your shoes and socks at the entrance, you can’t enter by the South and go out by the West. you need to go back to the South to get your belongings back. And from the South entrance to the park, it is a 10 minute walk. Depending on the energy left after the previous visit, you can walk or take a taxi, it will cost 1000 Kyat (1 USD).
It’s a quiet place, relaxing and well maintained.
The fountain with the elephants is quite famous and you will see it very well on the video below :

The Shwedagon Pagoda
Saint-Mary’s Cathedral
Bogyoke Market
Inya Lake
City Hall and Independence Monument
Sule Pagoda
Lively Streets of downtown Yangon
Yangon International Airport
Shangri-La Traders Hotel