Although peonies bloom for a short time, their foliage is lovely until frost. I plant mine in prennial beds with many other plants and they do well. My Buckeye Belle is in front of a white clematis , has siberian iris and hosta to one side and peony Primevere on the other.
Heather

That sounds so pretty hmac. I can visualize the combination of flowers and it presents such a pretty picture esp. the contrast between Buckeye Belle and Primevere.

I do not have much experience with peonies placements so I cannot help you, linnea56. All of mine are grown in straight rows so it is rather boring.

I have a row of three shrub peonies along my S-facing border before the house. They are in front of two very large camelias and are flanked on either side by American violets. This gives a nice contrast of shape and color especially in the Fall. The peony leaves go bronzy-dark while the camelia leaves stay green. The flowers don't last all that long in the rainy Pac NW, so having such beautiful leaves is a big plus.

I just divided one of them into two more "babies" that I'm trying out in other locations as well.

I interplant mine with shrubs and spring bulbs. One small protected bed has two peonies in it which are overrun with hyacinths and crocus, and everything gets along fine. Peonies do well with deciduous shrubs such as old roses: the peonies make their growth and flower while the roses are still leafing out, then the old roses bloom after the peonies. Meanwhile you can let small annuals fill up the space for more green and variety. With such an arrangement you get spring bulbs, then peonies, then roses, then perhaps a rest in summer (or lilies, Japanese anemones, late blooming herbaceous flowers). Also Heather's suggestion of irises as companion plants is good for the contrast of foliage.
This is with my zone 8 flowering times. Also we have a stiff nourishing soil and very warm, sunny dry summers, so I can afford to crowd my plants rather so that they protect each other from the eccessive solar rays.
An additional note: I'm a big fan of planting for succession of bloom. Nature does this: on my walks through the countryside here I see flowers in March, different flowers in April, and still different flowers in May, all from trees, shrubs, perennials, annuals, bulbs, coexisting in perfect happiness. Yesterday I passed white anemones growing with late pale violets, and a wood populated with a colony of poet's narcissus. And in the poor rocky places saponaria and globularia, both invisible two weeks ago. Mother Nature is still the great garden designer.