Bannerman Park
This park was the first public park in St. John's, established in 1864. By 1891, it was fully landscaped as a Victorian park. It was then immediately converted to temporary housing (a tent city) for the newly homeless following the Great Fire of 1892, and since then has been slowly but surely restored.
Harbourside Park and the National War Memorial
It's not a big park, but it is the centre of the Downtown so it's quite busy and popular. It hosts our Memorial Day ceremony as well as lunch-hour music and theatre performances for workers in the Downtown. It's one of the only publicly-accessible stretches of waterfront in the Downtown.
Bowring Park
Easily the most famous and beloved park in St. John's due to its association with a greatly admired merchant family, heavily landscaped trails and swan/duck ponds, etc. It's an exceptionally beautiful park. Our annual equivalent of lighting the city Christmas tree is actually illuminating the trees in the park. They're switched on by the Mayor in a well-attended ceremony.
Pippy Park
This is the big boy - one of the largest urban parks in North America at 3,400 acres (14 km2). It has a lot of developed attractions - the fluvarium, golf course, trails, campgrounds, etc. but it also has a lot of undisturbed wilderness for hikers, cyclists, cross-country skiers, and so on.
Quidi Vidi Lake
The grassy, trail-lined shores of Quidi Vidi Lake are certainly the most popular casual walking/jogging place in the city, probably because they're so flat and easier for people than even just walking downtown. The lake also hosts the annual Royal St. John's Regatta, North America's oldest continuing sporting event.
Grand Concourse
All of these parks form important junctions on the Grand Concourse, an urban trail system that links just about every part of St. John's and its suburbs. Parts of it are literally just sidewalks on scenic streets, but most of it is comprised of river-side trails and more park-like settings.
And there are dozens of smaller ones in the Downtown and numerous other larger ones in the suburbs. They range from playgrounds on a typical lot along a suburban street to the quite extensive park system of Mount Pearl, which markets itself as "A City within a Park".