Tel Aviv has many museums to offer. The museums I personally think are must-see museums are:

ERETZ ISRAEL MUSEUM

If you have only time for one or two museums, this is the place to go. The Eretz Israel museum shows a wide selection of artifacts from biblical times throughout the ages.
http://eretzmuseum.org.il
2 Chaim Levanon St., Ramat Aviv, Tel. 03-641-5244. Bus No: 7, 7a, 13, 24, 25, 27, 74, 86, 274.
Open: Sunday – Tuesday, and Thursday: 09:00-15:00, Wednesday: 09:00-17:00, Friday and Saturday: 10:00-14:00. 

ILANA GOOR MUSEUM

Ilana Goor is one of Israel’s most creative, fruitful and successful artists. In her museum Ilana presents a very impressive private collection that has been hand-picked by her over the years. The Ilana Gur museum is situated in the romantic old city of Jaffa at a unique building overlooking the Mediterranean.
http://www.ilanagoor.co.il
info@ilanagoor.com
4 Mazal Dagim St., Old Jaffa, Tel. 03-683-7676. Bus No: 10, 46.
Open: Sunday.-Friday: 10:00-16:00, Saturday: 10:00-18:00. 
Adult                                    28 NIS
Student, IDF, senior citizen    24 NIS
Children over 4 years old        20 NIS
Please call ahead to make sure that there’s no private event at the place.

TEL-AVIV MUSEUM OF ART

Finally, The Tel-Aviv museum of art is a place you mustn’t skip. The museum always showcases interesting art of all genres from many different collections.
http://www.tamuseum.com/
27 Shaul Hamelech Blvd., Tel 03-696-1297. Bus No: 9, 18, 28, 70, 90, 111.
Open Monday, Wednesdy: 10:00-16:00, Tuesday, Thursday: 10:00-20:00, Friday: 10:00-14:00, Saturday: 10:00-16:00. Closed on Sunday.

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TEL-AVIV MUSEUM OF ART

 E-H Dictionary