Hi Lisa,
I agree with heading to the Dolomites. head to Cortina d'Ampezzo and then west across into the Alta Badia. The Val Gardena is the next valley over, with a drive over the stunning Gardena Pass. Even if most lifts aren't open, the passes in the area are a great way to get up close to the peaks. In the area between Cortina and the Val Gardena (about 1:30 drive time) are the Giau, Falzarego, Pordoi, Campolongo, Sella and Gardena passes.
For instance, this is our own "Best of the Dolomites Drive". It can easily be done in a day and covers drives over 4 Dolomite Passes.
It can be started/ended from any point really, but I'll use Alta Badia:
At Corvara, take the Campolongo Pass (SS244) to Arabba. From Arabba take the Pordoi Pass (SR48) towards Canazei. Before you get to Canazei, take the Sella Pass SS242 (or stop in Canazei and go back a bit to continue). Take the Sella Pass and at the end, get right on the Gardena Pass SS243 (they branch off one another) towards Colfosco/Alta Badia. There's a cafe/restaurant/rest stop at the "top" of the Gardena, Sella and Pordoi Passes. You'll also notice a few small places to park along the passes to get out and walk among the Dolomite peaks.
For some info and photo's of the passes, check out:
www.alpineroads.com/dolomites.php
Some are listed under the German and or Italian name:
Gardena Pass - Grödnerjoch
Sella Pass - Sellajoch
Pordoi Pass - Passo di Pordoi
Campolongo Pass - Passo di Campolongo
Rainy day options could include the old towns of Bozen/Bolzano (and the excellent exhibit on the "Ice Man" at the Museum of Archaeology) or Brixen/Bressanone (and another good museum, the Diocean Museum).
www.bolzano-bozen.it/en/
www.brixen.org
Hope this helps.
FYI: This statement that David posts too often is not true at all: "the Grossglockner Alpine Highway (opening in May) takes you across the second highest point in Europe". The Grossglockner is nowhere near the second highest peak in Europe.
Paul