I'm from Spain.. in fact i'm currently in it.. about 2 hrs from Barcelona. I haven't been there since becoming Vegan but I can give you a few hints.
Are you vegetarian or vegan, to start?
gazpacho will be vegan
a green salad should be vegan, make sure to ask if it has eggs or meat just in case. "Amanida Verda" (They speak Catalan primarily in Barcelona) "Sense ous, y sense carn." You don't need to worry about dressings--salad dressings aren't something spanish at all. We use olive oil and salt
escalivada is grilled veggies, and would be vegan--make sure to indicate again you want the dish without eggs or meat, just in case (i'd be surprised to see them there, but there are always wierd restaurants.)
baguette will be vegan, as well as most white breads. "Ous" is eggs "llet" (pronounced lee-et) is milk--you can always ask.
What I would definately do is go to El Corte Ingles, if not some actual health food store if you should find it, and buy some non-dairy milk to have at breakfast; I usually also buy cereal and fruit (even when I wasn't veg) when travelling cus eating out three times a day is tiring, but maybe thats just me.
If you're vegetarian:
Omlettes are quite good in spain. Pans & Co. has a potato omlette sandwich, for your days on the go... It also will have a Bri sandwich, if Bri is vegetarian (I don't know which cheeses are and which aren't..)
Um, yeah, actually potato omlette is something very Catalan, so you can likely get it almost anywhere. Pastis de Verdures is really really good, and its this cake of vegetables and eggs and likely milk--was definately a favourite of mine before I went veg.
Barcelona has a decent vegetarian following so you wont have trouble finding restaurants there--Catalan food is not very veg-friendly though, if you're not in a veg restaurant... It's expected to have a first plate, which often can be veg. (and even then..) and a second plate, which is either "meat poultry or fish" typically...