We have been in Spain for the past 10 days (Barcelona, Seville, Granada, Cordoba and since yesterday in Madrid). As lacto- from Oregon, we have had to make an effort but it is quite feasible to eat well without compromising your dietary restrictions.
Fresc Co. is a growing chain of veg buffet restaurants in Barcelona (2 locations), Madrid (5 locations) and also in larger cities like Valencia. Great salad bar, along with pizza, pastas, breads, icecream, coffee etc. all for one price under 10 Euros. They do have some seafood in the buffet, so be sure to ask.
In central Madrid, we have already found two restaurants that are predominantly vegetarian - Artemisa and Dosa Grill Cafe.
Try Indian, Chinese, Italian, Mid-east restaurants. Even with functional knowledge of Spanish, we were able to make a special request for veg dishes (be sure to explain sin carne, sin pescado, sin avia...)
Supermarkets (such as in the base of El Ingle Cortes chain) are another choice to pick up all sorts of veg stuff (try Gazpacho, Vichysoisse... in cartons), and open air markets are a great place for fruits, nuts, cheeses etc. The fruits here are delicious compared to the US. Try the fresh squeezed orange juice. If you eat dairy products, there is a wide range of yoghurt and cheeses available.
Have a great veggie trip.
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