Housed in a sprawling medieval palace in the stylish neighborhood of El Born, this museum is a must-see. Every Sunday after 3 p.m., admission is totally free. Yep, admire Picasso’s “Las Meninas” series up close for zero dollars. The best place to experience the vibrant energy of Barcelona is Barceloneta Beach. Anything goes at this playa, where vendors hawk mojitos and margaritas and topless tanning is the norm. Bring a towel, scope out a spot in the sand and bake in the Mediterranean sun (with 50 SPF, of course).