Is there a way to assess the value of old vinyl records?

Given the OP’s time constraints and the unlikelihood of finding a real rarity, selling them to the record store or giving them to a person who actually cares were the best options. Most old stuff is just old stuff. I was very sad to discover that the 78s I inherited from my grandfather were worth nothing, but I mounted them on the walls as decorations. There you go–looked cool, reminded me of family.