Lost in Rain
Brothers a Tales of Two Sons
Puyo Puyo
Tetris
RiME
Lost in Shadow
Journey
Flower
Attack of the Friday Monsters
Crossniq+
Pilotwings 64
NiGHTS Into Dreams
Any Animal Crossing
Nintendogs
Point and Click Adventure games. Grimfandango or Journey Down are some of my faves. Zack and Wiki is another.
Chibi Robo
A Boy and His Blob
Endless Ocean series
Daytona USA (few racing games feel as chill as this IMO)
Shenmue does have combat but sparingly and walking around the small town has always been one of the most relaxing games for me. Just the first one not the sequels.
Toy Commander. Sorta does but it's chill.
Outrun 2006
Lastly a little odd one but Grandia. Yes it's a JRPG but it's pretty easy and the characters and sense of adventure never let the game dive into that typical drowning in melo drama. It's just one of the best games to give a great sense of adventure.