So many choices...
First go: something like this...
Sicily - Couple of days...Went there last easter and it's very nice, head up Etna for some beautiful views and a live volcano + snow (get the right hotel and you can see the lava from your window!
Alghero, Sardinia - Couple of days... Not been yet but it's somewhere I really want to go, scenery, beach and culture.
Pisa - (one or two days) You can't go to italy without seeing the Leaning Tower of Pisa (and a few other towns and very nice cave system near it)
The "Italian Riviera" - (overnight) Again Beautiful Scenery and the motorway trip is stunning, just tunnel after bridge after tunnel.
Arles and the Dordoign (sp) - (few days) Beautiful marsh area with wild horses and then up to the highlands with gorges and have fun cayaking down the river.
Swiss/Italian lakes - (Day or so) again a beautiful landscape and you can go swimming in the lake
Black forest - (day or so) The Swizerland you heard about in your childhood, except in Germany... Forests, clocks, cute cottages, clocks, lakes, clocks... you get the point.
Luxumbourg - (day) See the castle and massive gorge running through the city! then a nice hop to the channel.
I think that would be a quite nice trip, although the first few days may involve a few flights/ferry trips.
EDIT: Actually you could stick a day or two skiing or winter sporting in there by nipping to Chamonix or one of the resorts before going to the Black forest.