Anyone can do Heritage Quests but they do give huge status points also.
Here's a few to get you started -
J-Boots, start at level 15, Cru Naseto by NQ gate in Antonica.
Greater Lightstone, start at 15, kill Lightbringer Wisp in Commonlands to get the starter.
Dwarven Workboots, level 20, Hwal Rucksif at Ardent Keep in Antonica.
Ghoulbane, level 8, Vida Sweeps in Nettleville. When you get the Dusty Blue Stone keep it til you are level 20, then examine it to start the Ghoulbane quest.
Glowing Black Stone, Fishbone Earring and Shiny Brass Halberd start at 25, and there are others which start at higher levels.