The Museum of Contemporary Art is situated in New Zagreb, just accross of a shopping and entertainment mall Avenue Mall and was open in 2009. Young! Easily reached by tram number 14 from Jelačić Square. Alternatively, take a bus Nr. 219, 220 or 221 from the underground bus terminal under Hotel Esplanade.
This museum is not frequented often by tourists as it lies on the outskirts of the town, but believe me it is WELL WORTH visiting. Impressive exhibitions will impress you. Allocate at least 3 – 4 hours here to finish walking around comfortably.
The themes of the artworks were very clear – Democratization of art, art as a social fact, art through words etc and the art pieces are always thought-provoking.
Definitely pay this museum a visit if you have time.

Fun museum Zagreb
The collection is huge, a bit dark at times but overall really interesting. There are English translations for much of the text about the works so getting around is easy. They have 2 big slides that are a center piece of the museum. Entrance fee is 30 Kuna per person.

Museum of Contemporary Art
Position on google map:https://www.google.hr/maps/place/Muzej+suvremene+umjetnosti/@45.778861,15.9796218,17z/data=!3m1!4b1!4m5!3m4!1s0x4765d5d5562f6771:0xc8ab124bfcfd3d54!8m2!3d45.778861!4d15.9818105