Catalonia has a great variety of different landscapes very close to each other, mountains on the Pyrenees (at the border with France), green hills on north of the country, agricultural planes on the west and beaches on the east.
What to visit;
Montserrat - A unusual rock mountain, with a Sanctuary on top. It is very popular among Catalans. You can travel there by train (take Ferrocarrils de la Generalitat from Plaça d'Espanya to Montserrat-Aeri) or by bus (they leave from the Plaça de la Universitat in the morning).
Volcanoes near the city of Olot, and La Fageda d'en Jordà, a very nice forest and extinct volcanoes.
Adventure sports (in a lot of places in Catalonia like Llavorsí in the Pirineus)