Not sure about the weather for November in Peru, I climbed around Huaraz and in Bolivia (including an fun little sport crag right in La Paz) for a few months from June - September last year and weather was perfect. The highlight was climbing the regular route on "The Sphinx", a big wall a few hours from Huaraz. I also spent a couple of weeks climbing and putting up new routes at Hatun Machay, a great new area for sport climbing (at 4000m) also a couple of hours from Huaraz. This beautiful area has a good hut and also has plenty of quality easier climbs (from around 14-18 but others go up to 29ish) that help ease you into the higher altitude
I think the quantity and quality of established rock climbing areas in Argentina and Chile make them more desirable destinations for a purely rock climbing trip, particularly if you're looking for easier things at low altitude. Peru's amazing culture and the possibilities for great mountaineering also make it a great climbing destination.
The weather in November in Frey (near Bariloche) may still not be that good, but there are plenty of other good crags (mostly sport) to visit if you have transport, such as Valle Encantado. Los Arenales is great but up at 3000 - 3500m and may also be a bit cold and snowy at this time of year.
Quite a few places (sport and trad) to go near Santiago de Chile, and although on the other side of the continent, Brazil also has tonnes of well-developed climbing areas. Including Rio, where you can climb with amazing views over the city during the day, go for a swim at Ipanema beach as the sun sets, then go out for caipirinhas and samba in the evening!!