A 2009 survey recognized Vilnius as the greenest capital in Eastern Europe. Furthermore, Vilnius air is the cleanest among all European capital cities.
To achieve this Vilnius urban planners intentionally skipped many areas during the city expansion. These are named "parks" but with limited landscapping some of them are in fact urban forests. They are now popular for strolling, dogwalking or enjoying a picnic.
The oldest of these pristine zones of Vilnius is right next to Cathedral and the Castle. Known as Sereikiškių Park and the Hill Park (Kalnų parkas) it includes multiple hills with good city views, among them the Pilies (Castle) Hill, the Hill of Three Crosses (Trijų kryžių) and the Gedimino kapo (Gediminas Grave) Hill.
Larger and equally popular is the 162 ha Vingis (Bend) park to the west of New Town, hugged from 3 sides by Neris river. A former nobility hunting ground it is now a major location for summer song festivals and also hosts a rugby stadium and a WW1 German cemetary amidst its greenery. Today Vingis park forms a part of north-to-south chain of green zones which separates pre-1940 Vilnius boroughs to the east from Soviet boroughs to the west. While Vingis park is developed, much of this "Green belt" is not and there are places where one may feel to be teleported to a countryside forest after walking merely several hundred meters from high-rise residentials.
A bit further from downtown the two regional parks within Vilnius city limits (Pavilnis and Verkiai) are much better for recreation as they host some impressive scenery (Pūčkoriai rock exposure), interwar military installations and 17th-19th century manors (see Suburbs of Vilnius).
The old cemetaries of Vilnius may compete with parks in their greenness but have a different aura. To contemplate you may visit the early 19th century hilly Rasos cemetary (Southern Vilnius) or the smaller Bernardinai cemetary in Užupis (Old Town). Both include elaborate tombstones and famous burials. Antakalnis cemetary (Antakalnis borough) is the burial place for 20th century celebrities, heroes and villains. If you prefer religious minorities there is an Old Believer cemetary in Southern Vilnius, Muslim cemetaries near mosques in southern Suburbs and a Jewish zone in Sudervė cemetary (Viršuliškės borough). Sadly many famous minority graveyards were razed by the Soviets, among them two Protestant and the main Jewish one. Under the Soviet rule the tradition to bury the dead along religious lines also faded and the modern graveyards accomodate people of all communities.
Following the trend set by Paris Vilnius establishes a "beach" yearly on the bank of Neris in the New City Center where various public sport activities take place. Swimming is however not allowed in the river there. But you may swim in Neris within city limits at the beaches of Valakupiai suburb north of Antakalnis. Other beaches are available at Balsiai suburb lakes. All of these are possible to access by Vinius public buses.