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This is very good value, particularly if visiting for more than 24 hours. You can purchase either a physical or digital card. Available for 24, 48 or 72 hrs. Time starts when you first use the physical card or activates the digital card in its app and expires at the end of the purchased duration (not calendar day). Includes free guided downtown walking tour. Free access to 23 museums and galleries around Bratislava region and discounts in some museums and restaurants. Price is reasonable and you are likely going to recoup the cost of the card on the first day just by doing the walking tour and two attractions.
Bratislavský hrad
The castle contains a Museum of Bratislava History, and a baroque garden. There is also a restaurant open till after the actual castle tours into the night. The general precinct area immediately outside the castle, including the vantage points of the city are usually always open during the daytime, and is free to access.
Farmaceutické múzeum
For a taste of visual arts, pay a visit to the National Gallery at the embankment between Starý most and Nový most with permanent collections of Slovak and European medieval art pieces, although the temporary exhibitions tend to be far more interesting.
Bratislava City Gallery is also a good pick to see displays of historical fine arts, paintings and sculptures along with interesting temporary exhibitions.
If you like modern art better, pay a visit to the Danubiana Art Museum on the southern edge of Bratislava. It is about 20km from the city center, so too far to walk. Take bus nr 90 from the National Theater, a taxi, or drive. It is located on the Gabčíkovo Dam, a hydroelectric power plant.
Permanent archaelogical collections.