No bagpipes but:
Kings of Convenience - relaxing and soothing without being banal
Agnes Obel - a modern take on classical music without being stodgy
Beach House - name suggests some sort of surfer punk but that's not all all what they are
The Be Good Tanyas - alternative country without trucks and boots (yes, I'm old)
Goldfrapp - specifically "Black Cherry", "Felt Mountain" and "Seventh Tree"
Hope some of these float your boat.