My sister had the exact same problem only she needed a narrow bezel on a 32 inch lcd.
She had 32 and a quater inch space avaliable.
She got the Sony Bravia. The only other option, was, iirc, the Panasonic.
I would start by checking out these brands in a 37 inch.
Be warned! Do NOT believe the published specs. Three out of four of them are wrong. You MUST go to store and measure it.