Frommer's One/Two/Three day tours look like this:
- Day 1: This is going to be a very full day, so make an early start at the Plaça de Catalunya. Spend the morning wandering down La Rambla to the Mirador de Colón beside the port. Return via the Placa Reial and explore the neighboring Barri Gòtic with its central Catedral. In the afternoon visit Antoni Gaudí's unfinished masterpiece, La Sagrada Família, and the Parc Güell before returning to the Raval and Poble Sec districts on the western side of La Rambla. From there, take the funicular to the top of Montjuïc for a fine view of Barcelona and its harbor. Explore the gardens and castle museum, and if there's time, pop into the Museu Nacional d'Art de Catalunya for a glimpse of the finest collection of Romanesque relics in Spain.
- On the second day stroll through the pond- and garden-filled Parc de la Ciutadella and visit the Zoo, time permitting. Then explore the narrow-laned barrio of La Ribera, with its Picasso Museum and imposing Santa María del Mar church, and walk down to the old (but gentrified) maritime quarter and beachfront of La Barceloneta with its modern adjoining Port Olimpic area. It's the ideal spot for an atmospheric seafood lunch. In the afternoon wander around Port Vell and explore the regenerated El Raval district.
- On Day 3 make a leisurely morning exploration of L'Eixample, the 19th-century district that expanded the city away from the congested Barric Gòtic and Ciutat Vella in general. This is where you'll find Barcelona's widest avenue, the Passeig de Gràcia, and greatest concentration of moderniste (Art Nouveau) architecture, highlighted by the Manzana de Discordia zone, where Gaudí's Casa Batlló, Puig i Cadafalch's Casa Amatller, and Domenech i Muntaner's Casa Lleo Morera are all so close they virtually shake hands with each other. Most famous of all is another Gaudí gem, Casa Mila (popularly known as La Pedrera) further along the paseo. Pop into Vinçon, the city's famed design emporium, for a descent to relative normality, and then continue up to the village-like district of Gràcia at the northern edge of L'Eixample. Return to have lunch in Casa Calvet, a restaurant housed in an early work of the omnipresent Gaudí. In the afternoon catch the Metro up to Pedralbes and visit its monastery and palace. Then continue up to Tibidabo by funicular for the best overall panoramic views of the city and coast stretching north toward the Costa Brava. In the evening wander into the adjoining Collserola Park, still high above the city.
I also want to go to Andorra (see separate post), but that's a full day trip to and from Barcelona. Rick Steves also suggests a side trip to Montserrat, which is another whole day trip unto itself.
According to the RailEurope site, the train from Barcelona to Madrid takes about 3 hours.