It depends on what you're interested in…
Big Alpine climbs? Sestriere and Colle delle Finestre are west of Torino towards the border with France and have been featured in both the Tour and the Giro. Farther south are Colle del Agnello (Col d'Agnel in French), also featured in recent years in the Tour and the Giro; or Colle di Fauniera, featuring a monument to Marco Pantani carved in local granite; or Vallone d'Elva with the road going right through the mountainside ridges up a dramatic gorge; one more valley south takes you to Colle della Lombarda (Col de la Lombarde in French),which has been featured in the Tour and Giro. In these Alpine valleys they speak Occitan, which is closely related to Provencal on the French side of the border. And towards the coast is Prato Nevoso, ski resort and Tour/Giro pass.
Food and wine? Piedmont's Langhe, famous for its Barolo, Barbera and Barbaresco wines is east and a bit south of Torino. It's covered with vineyards, orchards, scenic hilltop villages with castle turrets and church steeples to rival Tuscany. And around Alba it's foodie heaven, the place where the Slow Food movement got its start.
I'm partial to southern Piedmont because I run tours there (shameless plug)
agile compass cycling tours(/shameless plug).