Barcelona has an extensive public transportation system, including buses and metros, that can easily take you to all of these locations. A single ride on the metro or bus costs around €2-3 ($3-4 CAD), but purchasing a T-10 ticket for €10.20 ($14 CAD) gives you 10 rides which can be shared among multiple people. Keep in mind that walking is also a great option for shorter distances and allows you to explore more of the city on foot.
If you have more time, consider taking a day trip to Montserrat. If you have less time, skip the Museu Nacional d'Art de Catalunya and spend more time at other locations. Make sure to purchase tickets online for popular attractions to avoid long lines. Finally, be aware of pickpockets in tourist areas and keep your belongings close to you at all times.