A great way to spend a couple of hours in Quito is to enjoy the Botanical Gardens. The name is Jardin Botanico de Quito. The price for entry is very reasonable ($3.50 per person).
There a plenty of paths to meander through and just enjoy the day.
Once you finish your visit at the Botanical Gardens, you can continue your leisure walk throughout Parque Carolina (Carolina Park) or if you feel very adventurous you can visit the Reptile House also near the Botanical Gardens and maybe pet a snake.