In Barcelona, public transportation like the metro, buses, and trains are the best ways to get around the city. The T-10 ticket is the most economical option, allowing you to ride the metro and buses ten times for just €10. For the Montserrat day trip, take the R5 train from Plaça Espanya to Aeri de Montserrat, then take the cable car to the monastery. Round trip transportation and admission to the museum will cost around €25.
If you have more time in Barcelona, consider adding a visit to the Picasso Museum or Casa Batlló. For those short on time, skip Park Güell and spend more time exploring the Gothic Quarter or La Rambla. Also, beware of pickpockets in crowded areas and take precautions to keep your belongings safe. Lastly, don't forget to sample some of the delicious local cuisine like paella and churros!