Webpage for the Portuguese train company, in English.
Webpage for the Spanish train company Renfe, which hasn’t really bothered with an English version (in theory they have, but they have only translated a bit and as soon as you select a route, it reverst).
Eurail visitor passes includes an option covering Portugal+Spain.
For some previous threads on Barcelona, this thread has some information and links to previous ones. Both matt_mcl and myself tend to pop up in these threads.
Often you will find that cercanías/rodalies are about as fast as the fast trains: the main difference is in the comfort level and the routes. There are trains from Barcelona to Valencia (an eminently visitable city - oh wait… oh, good, you won’t be there for Fallas; Fallas are great if you like them but every hotel within 200km is full), I suggest spending at least two nights there. The lonja (central market) is a rare example of civil gothic; the main train station itself is Modernista; the Ciudad de las Ciencias is both ultra-dupa-modern and, if you like science museums, quite cool (as well as cool in the temperature sense, which in May can be a plus).
From Valencia you can either continue down the coast or go to [del]the spider’s lair[/del] Madrid, perhaps with a stopover in little, tranquil, pretty Cuenca. The sight of the river gorge from the “hung houses” containing the Modern Art Museum is not for the faint hearted.
Two inland Andalusian cities which you may want to consider (I’m not familiar with either the coast or the Andalusian capital, Sevilla):
If you plan on stopping in Granada, take into account that tickets for the Alhambra MUST be purchased IN ADVANCE. As in, way in advance, not the day before.
I was in Córdoba last May: it’s time for the local Feria, definitely worth a visit. It’s less famous than Sevilla’s, but also a lot more visitor-friendly. We went to visit Medina Azahara, there’s a guy in a roulotte outside selling drinks. He told us it was the best time to visit, as it “hasn’t gotten too hot yet.” When we pointed out that the previous day had hit 40C, he laughed and said “well, yeah, but only for two hours, see?” Ah yes. We did, indeed, see.
I always forget: a great way to eat relatively cheap, although following the Spanish custom of having a relatively heavy lunch and light dinner, is “Menú del día,” a short menu whose items are already cooked (so, less waiting time) and, if applicable, the ingredients are fresh. If you’re asked whether you’ll be asking “from the menu”, make sure to say “from menú del día” - otherwise they may give you the regular menu.
And for most things you’ll find that a good rule of thumb is “normal time plus two.” In other countries, people eat between noon and 2pm: in Spain, between 2pm and 4pm. Movie times? The same. Dinner times? The same. Usual opening time for museums and stores-other-than-supermarkets? 10am.