I would suggest Halligye, but it's probably closed now.
Chun Quoit, and the hillfort nearby are easy to find, even if it's a long walk.
Ballowall Barrow (Carn Gluze), because it's just totally unique.
Chapel Carn Brea... the Entrance Grave on the top isn't in the greatest condition, but it's got atmosphere.
Carn Euny, as it's the most chilled place ever (or so I think), and you could walk to the ruined hillfort of Caer Bran. Sancreed Beacon's pretty close too, and has gorgeous views on a clear day.
Also, the fort on Trencrom Hill... the views are amazing.