What is the value of a Remington 760 257 Roberts?

Of course it depends a lot on condition, originality, etc., but generally speaking you'll not see too many for less than $500, and some will be in the $750 -850 range. The Remington website lists years of manufacture for the 760 in 257 Rbts. as 1954-1961. There was a deluxe version, with a checkered pistol grip and forearm (as opposed to the smooth grip and groved forearm of the standard version) and sling swivels that will command a premium.