There's a lot of nice trails around S.C. de Bariloche and San Martin de los Andes. I went there on a MTB trip there almost 30 years to the day ago (PA folded when I as down there) and really enjoyed it.

Did El Chalten 2 decades later but didn't hike though I understand they are nice. About 2 hrs from FTE to El Chalten (lot of dirt road back in 2003). There seem to be interesting hikes near Salta and S.S. de Jujuy (and Cafayate) but altitude could be problem.