Lots of options out there. If you're looking for a neck that is similar to an acoustic, and a guitar that is going to have some of the same characteristics, I'd look at a semi-hollowbody. I have a Gibson ES-335, and it has more acoustic qualities than you'd get from a solidbody, and Gibson offers the 50's rounded neck that is a bit thicker...more like a standard acoustic neck...at least the ones I'm use to. I prefer the rounded necks, and opt for them myself. With the 335 I can get some very nice clean tones as well as dirtying it up when called for. They're not cheap, but well worth it...a very solid guitar.
Here's a shot of mine...
