Your choice! People walk in wearing tourist attire; causal. I, personally, have gone for lunch in business attire. I've gone for dinner on dressy jeans. I've also gone after a formal affair or before dressed in a gown. For the most part, I would say "dressy-casual". Personally, I don't think "shorts & t-shirts" are appropriate, but I have seen MANY tourists walk in dressed that way.
You can dress up or go casual. It all depends on how you and your guest want to dress. From special occasion to just an intimate meal with your special loved one. Mary Mahoneys is the place to go for a delicious meal.
Casual
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