The 2009 Sony W, Z (and XBR) have very thin bezels. The 46" W is only 43" wide, and the Z and XBR is only 1/8" wider.
$2800 will be a bit tough though, but you can find the 46W5150 for $1050.00 right now
here , so that's pretty close, and if you keep an eye out maybe less if you're lucky.
If you look at the CNET video review
here , it gives you somewhat of an idea how thin the bezel is, it's only 1.5" on the top and sides.
The 2009 Sony V and S series have thicker bezels (44 1/4" wide) and the 2010 Sony EX series is about the same (44 3/8") , however they would be in your price range. Even at Best Buy (usually not cheap) the 46" EX400 is $899 online (could sometimes be cheaper in store)