We only had three days to explore both Barcelona and Montserrat, but we crammed a lot in and I can speak for our entire group, we fell in love with Barcelona. Although we were all very tired from our long flights to Spain from California we managed to make it to La Rambla our first night to experience some of the nightlife in the city, check out the Columbus Monument and even caught a very popular traditional Flamenco show (think Hawaiian Luau, but in Spain and with Sangria instead of roasted pig).
The next day we all took the "Hop On, Hop Off" bus tour of the city. We started by visiting the cathedral that will still be under-construction for the next 14 years - it started in 1882 (Sagrada Familia). Next we got off the bus at a park/community designed by Gaudí (Park Guell) and did a drive-by of the 1992 Olympic Stadium and many more cool sites. My parents and another couple also took the opportunity to walk along the Mediterranean Sea, get our feet wet and eat tapas. Beyond tapas I also enjoyed some Paella while in Spain, definitely one of my favorite dishes.
Montserrat. This mountain town is home to a group of monks (sadly not the ones who make Chimay), an impressive church, the "Virgin of Montserrat" (who many idolize and believe can heal them if they touch it), and some great views of the valley below.