Photo: Photo: Andreas Praefcke, CC BY 3.0 via Wikimedia Commons
Two locations: Wiener Philharmonikergasse 9, and Mönchsberg 32. The Salzburg Museum of Modern Art is on the cliff overlooking the old town. It houses contemporary art works from the 20th and 21st centuries, along with rotating international art displays.
The Museum der Moderne Salzburg has two buildings in Salzburg, Austria. The Rupertinum in the old town for new artistic concepts opened in 1983 and the Museum on the Mönchsberg for modern art in a contemporary setting opened in 2004.
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Mozart's birth house
From 1747 to 1773 the Mozart family lived in this house in the heart of Salzburg, where W.A. Mozart was born on 27 January 1756. The house is now a popular museum devoted to Mozart and his family, with interesting memorabilia and letters. Well worth a quick visit.
A long yet narrow street running parallel to the river in the centre of town, with lots of shops, famous for the old (or old-style) signs of profession outside each store.
Residence Gallery Salzburg, Domquartier
Art gallery showcasing European paintings from the 16th to 19th centuries. Established in 1923 to revive Salzburg's artistic heritage, the gallery's notable collections include the Czernin Collection, featuring 17th-century Dutch, Italian, Spanish, and French masterpieces, and works from the Schönborn-Buchheim Collection, highlighting Dutch and Italian artists of the same era. Some of the more famous painters include Rembrandt, Carel Fabritius, Carlo Saraceni, and Hieronymus Francken II.
Various shops in this area are quite old and impressive. For instance have a look at the interior of the pharmacy called Fürsterzbischöfliche Apotheke. No pictures though, this is a pharmacy not a tourist attraction.
Petersfriedhof
Perhaps most remarkable are the small catacombs (€2 adults, €1.50 children) carved into the nearby cliff side. Climb up for a couple of small chapels and a nice overlook.
Salzburger Dom
In Cathedral Excavations Museum you can see objects excavated from a Roman villa and foundations of the west towers of the Romanesque cathedral both of which stood in the area of today's cathedral.