Gaudi architecture, including the Parc Güell, the still unfinished Sagrada Família and the houses; La Pedrera/Casa Milà and La Casa Batlló.
Park Güell. This is on a hill overlooking Barcelona, so expect a relatively steep walk to the top (Lesseps metro station, then follow arrows which are met every 300 m); you will be rewarded with a panoramic view of the whole city. The park has two distinct parts, a relatively undeveloped natural area near the top of the hill, and the more famous (and crowded) sculpture park below. The sculpture portion is full of walkways and other structures exhibiting the distinct and colorful style of Gaudi, including the famous terrace. Free entrance.
La Pedrera - entrance (Diagonal metro station) costs approximately 8 Euro.
Sagrada Família Crucifix
Sagrada Família - To get up to the tower by elevator costs 2 Euro (long queues). Previously, it was possible to go up the spiral stairs, but now they only allow you to get back down. The most impressive thing is to see Sagrada Família at night with lights on, this is the time when you understands why people say that it is built of bones. Entrance costs 9 Euro. Sagrada Família metro station.
The Ruta del Modernisme takes you round all the best Modernisme (art nouveau) buildings in Barcelona. The main part of the route can be walked in a couple of hours, providing you don't stray too far from the main routes. The Tourist Offices offer a pack which includes discounted tickets to many attractions such as La Pedrera and Casa Battlo. All can be seen from the outside for free.