This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
If someone wanted to avoid the hassles of carrying gear and just wanted
to find a nice town for some day trips, my first choice would be
Cortina d'Ampezzo, Italy. Situated in the heart of the Dolomites, Cortina
has incredible, and I mean incredible, scenery and many great passes(don't
miss the ride up to the Tre Cime de Lavaredo, it's a great walk to
circumnavigate the base as well). You can plan trips from 30 to 150+ miles
of some of the best riding in the world.
My second choice would be Andermatt, Switzerland gateway to the Susten,
Furka, Gothard and Oberalp passes and close to Wilhem Tell's birthplace(he
didn't really exist but, there's a monument anyway). The day rides here are
longer and more strenuous but, you won't be disappointed.
Also recommended is the northern Italian town of Bormio. The Stelvio,
Gavia, Bernina, Foscagno and Mortirolo are all within a day's ride.