Hi,
@olive! I'm vegan and Y&Y is one of my go-to places. You're a vegetarian, so you have even more choices, like the wok-fried string beans, which are fantastic (but not vegan, so they're not in my current plan, but they are vegetarian).
My fave item there is the sweet & sour. It's listed as chicken, but they will make it with tofu instead--you have to ask to speak with the specialty chef--and it's really wonderful. Comes with very tasty rice. Filling, pretty, and delish.
There are a couple of other chicken dishes they'll make with tofu instead. I believe they have a miso chicken dish that you can get tofu instead of the chicken with.
Enjoy!