Vegetarian with no onion or garlic
Wow.. this one could be rough for you. Vegetarian, yes, but the additional restriction of onion and garlic might be tough. You could try getting on the phone with some local vegetarian restaurants (I'll list some below) and see if they have anything on the menu that works for your sisters.
Have you thought about trying the totally vegetarian Bamboo Garden near the Seattle Center? I think it's just ok, but it seems the menu would most closely match the dietary restrictions of your sisters. You, however, might be restricted because there is absolutely no meat on the menu.
Also, here are my two favorite veg restaurants: Carmelita in Greenwood and Cafe Flora on Madison. Again, no meat on the menus. Really, though, the dishes are so well crafted, you don't miss the meat (spoken from the view of a meat eater). Both restaurants are stylish and have great service.
I had one of the best calzones in my life at Carmelita last year (I still remember it oozing onto the plate when I cut into it). The atmosphere is very urban granola-ish and the tables are too close together to have an intimate dinner, but I like it.
Cafe Flora is similar to Carmelita in atmosphere. They list an amazing selection of non alcoholic herb infused iced teas and lemonades... I was completely impressed.
Hope these suggestions help!