Either in full sun or part shade. But, what exactly do these terms mean?
Full Sun
Full sun: an area that gets more than 6 hours of (continuous) direct sunlight each day.
Planting your peonies in full sun generally means that they will bloom somewhat earlier (than the same peonies planted in part shade). However, they will probably also need to be watered more often, and the colours of the blossoms will fade more quickly.
Part Shade
Part shade: an area that gets dappled light and shade throughout the day, or, an area that gets some direct light every day but fewer than 6 hours of (continuous) direct sunlight.
Planting peonies in part shade means that they will probably flower somewhat later, and that they will produce fewer blossoms (than the same peonies planted in full sun). However, the individual blossoms will usually last longer, as will the overall blossoming season, and the flowers will be unlikely to fade much.
Background
When choosing a location, please also take into account the background. If you are planting white or pale pink peonies, they will stand out best against a dark wall or fence. Conversely, if you are planting deep red or maroon peonies, they will look best against a white or pale-coloured wall or fence.
How Far Apart?
Plant peonies at least 2 feet (60 cm) apart — some would say that 3 or 4 feet (100 - 120 cm) is even better. Similarly, plant them at least that distance away from a wall or fence. Peonies need lots of room to grow: a mature peony plant can have a diameter of 3 feet (1 metre), or more.
When to Plant
The best time to plant peonies is very late summer or early fall. This is particularly true of "root stock" (or peony "divisions", as they are sometimes called). Peony plants which have been grown in a pot can be planted at other times of the year, such as late spring or early summer.
