I'm afraid you'll not have a strictly vegetarian place, but some restaurants as "l'Elefant" (San Bartolomé, 8 Sitges) have the option of a veggie menu. You can get more info here: http://www.sitgesrestaurant.com
Most places will offer you vegetarian dishes as well. You can try some typical Catalan dishes as Escalivada (baked vegetables), Calçots (kind of spring onions with a sauce made with olive oli, tomato, red peper, garlic and nuts)... A very typical dish of the area is Xató, a delicious salad, but it includes salted cod and anchovies as well, you can ask for it without these ingredients.
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