The two most popular day trips from Barcelona are to the Montserrat mountain nearly 40kms to the north of Barcelona and the Sitges beach in Tarragona to the south or the equally popular Lloret de Mar beach in Costa Brava to the north (see below for details on how to go to Lloret de Mar).
Montserrat ( in Catalonia) Although there are day excursions to Montserrat from Barcelona you can easily do it on your own by taking a train from the Plaza Espanya FGC station. There is a train hourly from 08h46 onwards daily though you have to decide which of the two options - by cable car (Aeri ticket) or by funicular (Cremallera ticket) BEFORE you buy the train ticket (the price is the same whether you continue the train trip on cable car or the funicular). In either case look for the R5 Barcelona-Montserrat-Manresa line at the Plaza Espanya FGC station (which, by the way, is huge so give yourself ample time) and just get off at the "Monserrat Aeri" Station if you are taking the cable car OR the Monistrol station if you are taking the funicular to Cremallera de Monserrat, which is at the doorstep of the world-famous Montserrat Basilica.
The square in front of the Basilica at Montserrat. The "Cremallera de Monserrat" funicular station is on the left-hand side of the picture. On most days at 13h00 sharp the Montserrat children's choir, one of the most ancient in Europe, appear to give a recital in the Basilica. The 10-minute performance is well worth waiting for.
The entrance to the Montserrat Basilica.
The courtyard at the Montserrat Basilica.
Sitges (Costa Dorada) Sitges is undoubtedly the most popular beach in Costa Dorada to the south of Barcelona and is fast catching up on Lloret de Mar, its rival in Costa Brava to the north. However, its reputation as a favourite haunt for gays (much publicized with the Sitges Gay Carnival in February each year) is driving many families away. An horchata (orxata in Catalan) seller there told me that another reason why business is falling lately is that many Spaniards are not coming to Catalonia anymore for political reasons. Yes, all that shouting for an independent Catalan is beginning to take its toll on local tourism.
The train from Barcelona to Sitges takes only 45 minutes. They are quite frequent (every 20 minutes or so) and you can take them from the Barcelona Sants station or the Passeig de Gracia station if it's more convenient to you.
An equally sandy beach but less crowded along the Costa Dorada is Castelldefels, which is even closer to Barcelona than Sitges. You can take the urban train also from the Barcelona Sants station or the Passeig de Gracia station to go there. But if it is a strictly quiet, family type of beach frequented by the locals and where your children can play in complete safety that you are looking for, then I would suggest that you go further from Sitges to Cunit whose beach is quite small and will save you lots of walking (if you are one of those who are looking for a relaxing day by the beach without too much walking or being surrounded by tourists!).
The eye-catching clock tower in the main street of Sitges.
Just a section of the beach in Sitges which extends for some 3 kilometers.
Lloret de Mar (Costa Brava)
As Sitges has become almost a gay territory, families with children who feel uneasy with the predominantly gay holiday-makers in Sitges might want to consider going to Lloret de Mar in Costa Brava to the north of Barcelona instead. The beaches in Lloret de Mar are just as clean as the ones in Sitges.
While there is no train from Barcelona that goes to Lloret de Mar (since there is no railway station there) you can take a train to Blanes and from there take a shuttle bus to Lloret. However, the less complicated way to go there is to take a Sarfa express coach from the Barcelona Estacio del Nord (North Bus Station). In June the first coach leaves the station at 08h00 and the second at 10h00. But check this website for a particular day as times vary according to the season (more frequent trips in July and August). The trip takes just an hour. At the time of writing the Estacio del Nord bus terminus is at No. 80, Carrer d'Ali Bei and you can reach it by getting down at the Arc de Triomf subway station (Line 1) and walking up Carrer de Ribes to its intersection with Carrer d'Ali Bei.