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I'm biased because I live there, but if you head south then I think it would be more fun going from Valence than Lyon. The 'terre froide' bit between Lyon and Grenoble is a bit dull. Lyon to Valence is only 1hr on the regional (TER) train, or there are occasional TGV trains Lyon St Exupery to Valence that take 35 mins. From Valence Ville or Valence TGV you can cross the Vercors to Grenoble.
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I disagree. Head due east from Lyon and you quickly hit the southern end of the Jura, and can ride climbs like the Grand Colombier, Mont du Chat and Mont Revard, all of which are interesting and scenic cols.
If you want to head south from there to Grenoble (and the Vercors) then you can go over the three classic cols of the Chartreuse, the Granier, the Cucheron and the Porte.
Planning on riding from Lyon to Turin and back this summer. Any mountains I shouldn't miss?