Tel Aviv is an energetic and somewhat gritty city, and traces its roots back only to 1909. That predates the establishment of the the State of Israel by a few decades, but still makes it virtually a new city and atmosphere-wise about as far away from the ancient walls of Jerusalem as you can get. Its early planners envisaged a garden city and the first Hebrew-speaking city, although today English and myriad other languages reverberate through its dense patchwork of streets.
Many visitors to Tel Aviv come and go with a stroll along the Tayelet Lahat (seaside promenade) or a dip in the Mediterranean as their chief souvenir, but the waters here run deeper than that: as a religious center the primacy of Jerusalem is beyond contention, but for most everything else, there's this city of 400,000 people that can sometimes feel much bigger than that.
Part of the reason for this is the outsized cultural life. The Tel Aviv Performing Arts Center is home of the Israeli Opera and world-class musical and dance performances. TAPAC, as it's also called, opened in 1994 and a newer wing houses the renowned Cameri Theater. Many productions feature screened simultaneous translation into English.
The Tel Aviv Museum of Art showcases works by greats like Picasso and Van Gogh and also has an impressive range of temporary exhibits featuring both Israeli and international artists. The main museum is located next to the TAPAC. The Helena Rubenstein Pavilion for Contemporary Art is a separate location.
Israel maintains something of a cultural edge where contemporary dance is concerned. If you have the opportunity to take in a performance of the Batsheva dancers or any other troupe at the Suzanne Dellal Centre for Dance and Theatre, don't miss it. The location in the heart of charming Neve Tzedek, Tel Aviv's first neighborhood (not counting ancient Jaffa) alone makes it worth your time.
Yes, Tel Aviv is an international city and has the artistic muscle and Madonna moments to prove it. But it's also an Israeli city, and there are plenty of cultural venues that highlight both Israeli history and Jewish heritage. An excellent place to start is the Land of Israel Museum (Eretz Israel Museum), which has fascinating exhibits of ancient coins, less ancient postage stamps, archaeology, ethnography and more.
The Beit Hatfutsot Museum of the Jewish People is located on the campus of Tel Aviv University in Ramat Aviv. A short taxi ride from central Tel Aviv but definitely worth the trip for the detailed exhibits which emphasize the continuity of Jewish culture throughout history.
Military history buffs will enjoy the Israel Defense Forces History Museum, located right next to the HaTachana marketplace.
Get an eyeful of Bauhaus architecture along Bialik Street and especially tree-lined Sderot Rothschild (Rothschild Boulevard) and catch a whiff of history at the Hagana Museum at no. 23. This small museum traces the early history of the Israeli military.
Beit Dizengoff, the simple home of Tel Aviv's founding mayor at number 16 Rothschild. It's where David Ben-Gurion declared the establishment of the State of Israel and is now home of the Independence Museum.