I really enjoy David Byrne's solo albums -- the one's I've heard at least -- but they're not really anything like what the Talking Heads did. The first solo of his I heard was Rei Momo, which is essentially a salsa album. I like it a lot, it's incredibly catchy, but it's pretty much basic salsa with David Byrne's English vocals.
My favorite albums of his are probably Uh Oh, Feelings, Look Into the Eyeball, and Grown Backwards. I'd probably just start with Grown Backwards, which came out last year, because it's the most cohesive and human album I've heard him release. There's something very emotional and real about the way he sings the songs on this album.
I think most of his albums take a world music angle -- I haven't heard his film compositions; and I haven't heard all of his albums -- but most of what I've heard is heavily influenced, especially Uh Oh and Look Into the Eyeball.
Grown Backwards really has none of that influence, though. One of my favorite songs on the album is actually a cover of Lambchop's "The Man Who Loved Beer". I like the original as well.