score:8
Stelvio pass is very close to Pass Umbrail. In fact you almost pass through Pass Umbrail when entering Stelvio from one direction.
Pass Umbrail connects to the Val Müstair, which, if you drive uphill, connects with the Pass dal Fuorn also know as the Ofenpass in German. This pass is in and around the beautiful Swiss National Park which has excellent day hiking.
Swiss National Park scenery near Pass dal Fuorn. Wikimedia Commons, Hansueli Krapf, Creative Commons Attribution ShareAlike 3.0
Upvote:5
A little bit further away (but still in the couple hours limit would be the Grimsel and the Furka pass roads.
The picture shows the view from the Grimsel pass road on the Furka pass road. If you cross the Grimsel, you will have quite a nice view on a lake and you can visit a fortress that's build there.
From there back to Italy (via Ticino), you could then drive over the Nufenen pass.
Upvote:7
Wikipedia in German has an extensive list of alpine passes. There are similar links in English and French but the German one can easily be superimposed on Open Street Maps, Google Maps or Bing Maps. You could use those maps to explore by yourself.
A few notable passes are: