The only synagogue in Bratislava.
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.