I've been hearing great things about the Bob Marley, Messenger exhibit at The Grammy Museum at LA Live.
The exhibit's focus is on Marley as a private, spiritual person and includes items from the personal collection of the Marley family.
While you are clicking around the museum site take a look at the public programs page. Homegrown is a series of shows featuring LA based musicians. Performances take place in the intimate, 200 seat Clive Davis theater. Tickets are available for upcoming shows including BET Awards "Best New Artist" nominee Miguel on June 28th and an evening with Todd Rundgren on July 18th.
The Grammy Museum is open Mon - Fri from 11:30 to 7:30 and on weekends from 10 am to 7:30. Take advantage of the fact that the museum is open late and visit before dinner or a show at LA Live.