Check out Tibidabo, there's the Sagrat Cor, Tibidabo amusement park, and a 360 degree view of Barna and the valley behind. It's quite easy to get there - metro to Tibidabo from Pl. Catalunya, tram or walk up to the funicular. If you walk up, look to your left when crossing the overhead bridge, you might see a submarine!

If you fancy a walk after Sagrada Familia, head north-west to Gràcia to see how locals live, walk towards Pl. del Sol's direction, there are lots of small tapas places along the way - most are cash only. After that, head down Gran de Gràcia, cross the Diagonal and down Rambla de Catalunya (not to be confused with Las Ramblas closer to the water).