The remains of Pirita Klooster (Pirita Convent), dedicated to St. Brigitta are definitely not an obvious place to visit. I have walked around dozens of times but never realized there was something interesting except for one old wall seen from the road. Until just a couple of years ago when I accidently ended up inside and was positively surprised – those old ruins are absolutely beautiful.
It looks like a perfect setting for shooting some medieval movie or a series like Games of Thrones (and this place actually was used as a shooting location for some historic movies a couple of times). One more good thing – it’s a rare location where you can walk alone, without being accompanied by crowds of tourists unlike in Old Town. Usually there are no more than just a couple of other visitors hanging around.
Little tip: it seems that the tickets kiosk is closed for the cold season, so currently entrance to Pirita Convent during opening hours is free.