The Israel Museum

11 Ruppin Avenue, Givat Ram – The biggest and most important museum in Israel, and one of the ten largest museums in the world. In the museum, one can find fascinating collections in the fields of archaeology (including exceptional revelations such as the Judea desert scrolls, and ancient and rare handwritten copies of the Bible), ethnography, Judaica, Israeli art, and world art. The museum also hosts several branches – the Rockefeller Museum of Archaeology, the Ticho House, and the Pali Art Center. The museum's beautiful sculpture garden is spread over approx. 20 dunams (20,000 sq.m.), and features special lighting at night.
The museum's website:

Yad Vashem

Har HaZichron, Jerusalem – Yad Vashem is an institution dedicated to commemorating the Holocaust. It was established in 1953 by the State of Israel. Since its inception, Yad Vashem has included a Holocaust Museum, exploring the history of the Holocaust through pictures and different exhibits that represent the period, including the rise of the Nazis, the ghettos, the concentration camps, the uprisings, and the release of the final survivors.
In 2005, after a construction process that lasted approximately 10 years, the new museum, which operates side-by-side with the old museum, was opened. Together, these two comprise the largest Holocaust museum in the world. The structure of the new museum is arrow-like, penetrating the mountain on one side, and emerging from the other side. The museum presents the story of the Holocaust through many media: original objects, documents, testimonials, movies, diaries, letters, and artworks.
Yad Vashem website:

The Artists' House

12 Shmuel HaNegid, Jerusalem – A vibrant exhibition center offering a unique and varied mixture of Israeli and international art. The annual exhibition program includes a series of outstanding young artists presenting their work for the first time, a retrospective series for veteran artists, topical exhibitions, combined exhibitions for Israeli and international artists, and a variety of extra activities.

Tower of David Museum

The Tower of David is the nickname given to the fort that defended Jerusalem for hundreds of years. The fort is located at the highest point of the Old City, and from the high tower you can see the whole of Jerusalem. In 1989, the Tower of David Museum opened, displaying the history of the city. The prominent exhibition includes visual displays depicting different events from the long history of the city – each room of the fort is dedicated to a different period. In addition, the museum presents rotating exhibitions, and also environmental artworks. Concerts and public events are often held in the courtyard, which is filled with archaeological discoveries.

Rockefeller Museum

27 Sultan Suleiman St., Jerusalem (near Herod's Gate) – The Rockefeller Archaeological Museum, which opened in 1938, is located in a building which can be regarded as a milestone in the history of East Jerusalem. The museum contains many important historical artifacts from the Jerusalem area, as well as from other areas of Israel. The museum building displays an impressive collection of antiquities unearthed during excavations that took place in Israel during the time of the British Mandate (1920-1948). Prominent findings include a collection of gold jewelry found in Beit Shemesh and Tel el-Ajjul, Megiddo ivories,the Lachish Letters, Umayyad-era wood panels, and decorative wood lintels from the Church of the Holy Sepulcher.
The museum’s page on the Israel Museum website:
West Meets East – The Story of Rockefeller Museum

The Menachem Begin Heritage Center Museum

6 Nahon St., Jerusalem – The Menachem Begin Heritage Center Museum creates an experiential encounter with one of the most important chapters in Israel’s history, while introducing visitors to Menachem Begin, who was an Irgun commander as well as the leader of the Herut and Likud political parties, before becoming Israel’s sixth Prime Minister. The museum takes visitors on a journey through time, including reconstructions, original artifacts, documentaries and other films, interactive touch screens, dramatic lighting, and a background soundtrack. By telling the story of Menachem Begin’s life, the museum offers visitors a historic encounter with the most dramatic and moving moments in the history of the State of Israel, and the seminal events that have helped to shape its character.
Museum website:

Bible Lands Museum

25 Granot St., Jerusalem; the Museum Complex, Givat Ram – Jerusalem’s Bible Lands Museum features exhibits originating from places mentioned in the bible. This modern structure, situated in Jerusalem’s Museum Complex, contains one of the world’s most important collections of antiquities. Biblical stories are given an entirely new dimension when examining this collection of exhibits, which reflect the lives, beliefs, and ideas of the inhabitants of Middle Eastern countries thousands of years ago. The museum contains one of the world’s most important collections of biblical archeological artifacts, and its exhibits are accompanied by maps, sketches and bible quotes. It was established in 1992 by Dr. Elie Borowski (an expert on ancient texts) and his wife Batya, and features Dr. Borowski’s own private collection. The museum’s permanent exhibits illustrate the ancient history of the nations of the Near East region from the very dawn of civilization until the time of the Mishnah and Talmud (c. 500 CE). The exhibits, maps, and illustrations enable visitors to follow the structure and everyday life of these ancient civilizations, assess the importance and essence of religious rituals, discover ancient means of communication, and marvel at the artistic ability of the region’s ancient inhabitants.
Museum website:

The Science Museum

The Museum Complex, Givat Ram, Jerusalem – The Bloomfield Science Museum features changing exhibits in the fields of science and technology. The exhibitions are interactive, and encourage the visitor to not only view the exhibits, but also touch and activate them. The museum strives to showcase science as an inseparable part of modern society, and links science with everyday phenomenon.
Every year, on 14th March, the museum organizes an exhibition of teen science projects as part of a young scientist contest to honor Pi (π) Day.