As its name suggests, the Museu de la Catedral is located in Barcelona's cathedral. I've started with this museum because it provides a great introduction to the city's past and will (hopefully) give you an insight into how religion and the monarchy have shaped its development.
There are numerous works of religious art on the walls of the ancient chapterhouse, which stands next to the cathedral, with The Pieta by Bartolome Bermejo among the most impressive exhibits. You can also view a selection of items that are no longer used in ceremonies, with a baptism font from the 11th century and the monstrance - a stunning throne made of gilded silver - among the key pieces.
Museu d'Art Contemporani de Barcelona
My next choice is the Museu d'Art Contemporani de Barcelona (MACBA), which is a bit of a contrast to the previous establishment. This gallery hosts a collection of pieces that have been created in the last 50 years, with several permanent installations as well as a regular calendar of visiting exhibitions.
Among the artists whose works are being showcased at MACBA in 2013 are Hans Haacke, Helio Oiticica and Marcel Broodthaers. What I really like about this gallery is that there are daily guided tours, which are great if you want to learn more about the pieces on display, as well as regular debates and hands-on workshops for children.
This is one of the quirkier options I came across in Barcelona, with this museum dedicated to "the world of ideas, inventions and creativity". I think it's a must-visit while you're staying in a luxury city-centre hotel for several reasons.
Firstly, MIBA encourages visitors to come up with their own ideas for new inventions (there's a great range of bizarre and useless inventions to give you some fun inspiration). Secondly, the museum itself is designed to challenge your concepts of the world around you - a classic example of this is in the main entrance where you can walk across a sheet of clear glass that's intended to make you feel as though you're flying.
Finally, MIBA aims to make you think about the inventions on display and to alter your perspective to give you an idea of how companies and individuals come up with products or gadgets that have a big impact on society.
Centre d'Interpretacio at Park Güell
Park Güell is worth a visit in its own right, as it's home to some of Antoni Gaudi's most striking works. To learn more about the ambitious project, head into the Centre d'Interpretacio, which is located in the porter's lodge by the main entrance.
This stunning building displays plans, photos, models and information about the construction materials used in the park, as well as offering up interesting facts about the flora and fauna that lives in the area and suggesting walking routes for exploring the park at your leisure.
I think this is an excellent way to start a visit to Park Güell, as it means you'll have an even greater appreciation of the sculptures and structures you come across as you explore this little pocket of green space.
(Photo credits, top to bottom: [ThinkStock - iStockphoto] - [ThinkStock - Photodisc] - [ThinkStock - Fuse]