http://www.restaurantesvegetarianos.es/component/option,com_sobi2/catid,45/Itemi...
Al Natural - Vegetarian restaurant - Tarragona

Address: Arquitecte Rovira, 3
Location: Tarragona
Province: Tarragona
Telephone: 977 21 64 54

Els Agora Immortals - Vegetarian Restaurant - Tarragona

Local emblematic of the top of Tarragona
Address: C / Sant Llorens 14
Location: Tarragona
Province: Tarragona
Phone: 977 231 520

It also gives out one in Girona, Barcelona and Lleida depending how far you want to travel.

Hope this helps you find the needle in your haystack.
Rosie

Hey Wheelie,
This is a post (below)on the Indian restaurant in Tarragona,added by Jeff in 2011.I went there earlier this year & my meal was great & inexpensive.They do Veggi options.

  If you are visiting Tarragona, you might like to try this very friendly Indian restaurant, which offers traditional biryanis, baltis and curries plus some pizzas and pasta dishes.

We tried poppadoms and onion bhajis (huge!), followed by chicken Madras (acceptably hot for UK tastes), a very tasty lamb Rogan Josh, basmati rice and nan-type bread (they don't seem to have a nan oven but remember we are in Tarragona).

For dessert, a kind of rice pudding with nuts and some interesting green raisins. With four Indian Cobra beers, coffee and rum chupitos our bill came to 39 euros for two, but you could easily eat for less. Various Indian vegetarian dishes. Portions are modest.

The decor is attractive and Salou veterans Said, Kamal and the lovely Lluna all speak excellent English and are really attentive and friendly: we felt very welcome and will definitely go back.

They offer wifi, a large screen TV also do a Bollywood evening so best start practicing your moves before you go

Ramón y Cajal, 51, 43005 Tarragona. Near the bus station and the Parc Central/Eroski shopping centre, and about 10 minute's walk from the Corte Inglés and the Rambla. Tel. 977 220 847, massalarestaurant@yahoo.com

As far as I know the Indian restaurant n Tortosa closed years ago,but there is a small Pakistani cafe next to the Estate agents "My Spanish Home" in Tortosa.Not sure on Veggi options though.     Bon Appetit