The gravestone is located near the Barney Circus grounds.
The default phrasing on the gravestone reads, "Here lies "Mark" Rancher Extraordinaire Rest in Peace", though the name can be changed. In the original Japanese version, if you had connected your Friends of Mineral Town to A Wonderful Life (or More Friends of Mineral Town to Another Wonderful Life), the name of your AWL character would appear on gravestone since Harvest Moon DS takes place 100 years after the Wonderful Life's time period. Your Gamecube character has naturally passed away, leaving Pete (Pony or Claire, if you are playing Cute) in charge of the same farm, hinting that they are a decedent of the player's previous character.
However in the North American version, the gravestone reflects the name of your Mineral Town character instead. If your Mineral Town game lacks a save file when you connect it to DS or Cute, the gravestone's name will be left blank.