I wouldn't travel to see most actors-turned-musicians, but since I live near the Rams Head, I generally figure I might as well check them out if one of them comes through here, so off the top of my head I've seen:
Kevin Costner (and Modern West)
Billy Bob Thornton (and The Boxmasters)
Kevin Bacon (The Bacon Brothers)
Minnie Driver
The John Corbett Band
Ms. Driver is the only one that I went to see a 2nd time, although if Thornton came through again, I'd probably go again..... out of the above list, I'd say Minnie's the most musically talented, she sang mostly accompanied only by herself on an acoustic guitar.... the first time I saw her, she did what it seems like a lot of them do (in interviews or on stage), which is to spend a lot of time explaining why they're not just another "actor turned musician", that they're really musicians that got into acting as a sideline.... the 2nd time she just sang and played..... Costner and Corbett did the age old "play an acoustic guitar with a really loud band behind you so no one can really hear your weak voice and guitar playing", their bands were really the stars of their shows..... Billy Bob's show was probably the most entertaining, but that's probably not surprising...... the Bacon Brothers were pretty bland... not horrible, and they seem ok as musicians, but just meh......