In reply to DaveHK:
> Easter will severely narrow your options, its prime ski touring season!
As will June - anything remotely high will still have snow on north-facing ledges.
to the OP - Have a look at the Bavarian alps - fly to Munich and hire a car or use the trains. If you're thinking of easter or June then there's plenty of stuff of low enough altitude to avoid the snow. The webcams at fotowebcam.eu are useful as you can look back and work out when the snow goes.
Have you been to the alps before? If so, which bits?