Hi Richard,
My suggestion would be to visit the Dolomites as close to the end of your trip as possible and preferably have a car for your visit. Cable cars generally do not open this early, but one in the Val Gardena does open by mid May, this being the Mont Seuc/Seiser Alm cable car from Ortisei (Val Gardena) up to the beautiful Seiser Alm/Alpe di Siusi. You can walk (paved paths), hike or just soak up the amazing Dolomite scenery.
www.alpedisiusi-seiseralm.com/index.html
As where to base, that's tough. We like the Val Gardena and our stay at the Garni Ariston in St. Christina, but loved our two stays in the Alta Badia at the Ciasa Montanara in La Villa. The Gardena Pass (terrific drive among stunning, up close Dolomite peaks) connects (or separates) the Val Gardena and Alta Badia. Even though most cable cars are closed at this time, driving a few passes gets you up close to all the amazing scenery. There are plenty of passes to drive (Gardena, Sella, Pordoi, Campolongo, Giau, Falzarego, etc ) and stop along in a relatively small area based in either the Val Gardena or Alta Badia.
www.garniariston.com
www.montanara.it
For up close spectacular views of the Dolomites by car, 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 Val Gardena:
Head to Selva and over the amazing Gardena Pass to Colfosco and Corvara (Alta Badia). Here, take the Campolongo Pass to Arabba. From Arraba take the Pordoi Pass towards Canazei. Before you get to Canazei, take the Sella Pass (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 (they branch off one another) towards Selva and the Val Gardena. 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). There's also Klausen/Chiusa, Sterzing/Vipiteno and even Bruneck/Brunico.
www.bolzano-bozen.it/en/
www.brixen.org
We have photo's of our Dolomite trips, among others, at:
www.flickr.com/photos/pjbassplyr/sets
Paul