In reply to Pursued by a bear:
Auvergne holds a special place in my heart as all of my family comes from there
There's some good advice above (though the Gouffre de Padirac is in a different region!), but here's some more random suggestions:
-Going up Puy Mary and walking the ridge to the Brèche de Rolland is indeed super cool, not as impressive as the real brèche (gap) in the Pyrénées but still worth it. I remember walking as far as Puy de Peyre-Arse and going a long loop, can't remember where we started exactly but that wasn't at the Pas de Peyrol, way below on a kind of plateau with lots of blueberries (if you come at the right time of year). Ideally go early to avoid crowds on Puy Mary.
-If you've never seen hoodoos, there's a shortish hike in Boudes that takes you to the Vallée des Saints where you can see some, it's no Bryce Canyon but it's lovely nonethless!
http://www.auvergne-centrefrance.com/geotouring/curieux/vallee-des-saints-b...
-The Vallée de Chaudefour is not to be missed, it's a natural reserve with two superb pitons (with excellent climbing I'm told), the Dent de la Rancune and Crête de Coq. You can do a very long loop, hiking up the left side of the valley, walking the ridge to Puy de Dôme (very touristy) and hiking back down the right side. About 20km/1,000m elevation gain. At least make the short walk (30mn?) to the bottom of the valley. There's a signed waterfall (Cascade de la biche) on the left side as well worth the detour once you're in the heart of the valley.
-If it's cold in the mountains you want to head for the area around Issoire, you'll think you're in southern France already! Issoire itself is a lovely town with a beautiful abbey. On your way there visit Saurier, Saint-Floret (check out the upper reaches to see the church and the graveyard and ossuary).
-If you like churches, make sure to visit Saint-Nectaire, Saint-Victor-la-Rivière, Cheylade (not far from Puy Mary)
-Personnally I'd avoid Murol and Chambon-sur-Lac, unless you like crowds
-Every summer there's some sort of art festival called Horizons Sancy: it's a collection of art works scattered around in nature, some are very conceptual, others are interactive, it just depends. They can be fun.
http://www.avenue-web.net/_generateur/Documents/90/1/Horizons-Depliant-2017...
Hope the weather turns out alright for you, it can be cold and rainy up there (15C this week at 1,000m altitude)! But that's why it's so green
Oh yeah and check out truffade, Salers, Saint-Nectaire, Cantal, saucisson (best one is in Condat)... And perhaps the local granite, basalt and gneiss climbing.