Tsuro is a very quick, Zen game. It's tile placement and stone movement.
Obviously if you don't like S.H., you probably won't like The Resistance or Avalon. But from the same publisher, there's Coup (a game of creative lying), and Grifters (an engine-builder made up of resource collection with a crime theme). I like them both and they're very quick.
I don't think Fluxx could lead to long term frustration, because it's just so wild.
Catan is a classic and it's never caused tempers in my group.