We discovered Carmela Ice Cream at the South Pasadena farmer's market; they've since opened a shop in NE Pasadena:

http://www.carmelaicecream.com/

It does sound like you are remembering the Grand Central Market at the bottom of Angel's Flight in Downtown LA, unless you can remember another part of town. There are a number of farmer's markets in SoCal throughout the week, though some are larger and have a wider variety of vendors.

Also in Old Town Pasadena is Bird Pick for tea:

http://www.birdpick.com/stores/