Menu Recs for Limon, Zarzuela?

Got some younger friends in town from LA, and wanted to show them some of the food that they don't get too much of down there. They don't eat much other than the major college food groups: pizza, burgers, beer, take out, mystery meat, mashed potatoes, more beer.

Any "must eats" or "don't waste your time" suggestions for dishes at Limon or Zarzuela?

Or, any general preferences between the two? Limon is in a more interesting neighborhood and we'll have plenty of bars to choose from afterwards, but parking's easier near Zarzuela!

I've been hankering to try both, but I'll let people's food preferences be the deciding factor.