Games like Button City
Games like Button City include Slime Rancher, There Is No Game: Wrong Dimension, Little Kitty, Big City, TOEM: A Photo Adventure, and Return to Monkey Island. We matched them by the tags players give Button City on Steam (Arcade, Point & Click, Funny, Adventure, and Narrative): closest matches first, and among equally close ones the better-known games.

Slime Rancher
Shared: Adventure · Exploration · Cute

There Is No Game: Wrong Dimension
Shared: Point & Click · Adventure · Funny

Little Kitty, Big City
Shared: Wholesome · Exploration · Cute

TOEM: A Photo Adventure
Shared: Adventure · Wholesome · Exploration

Return to Monkey Island
Shared: Point & Click · Adventure · Funny

Broken Age
Shared: Point & Click · Adventure · Funny

Deponia
Shared: Point & Click · Adventure · Funny

Donut County
Shared: Funny · Adventure · Cute

Botanicula
Shared: Point & Click · Funny · Exploration

Florence
Shared: Adventure · Cute · Story Rich

Frog Detective 1: The Haunted Island
Shared: Funny · Comedy · Cute

CHUCHEL
Shared: Funny · Point & Click · Comedy

A Hat in Time
Shared: Funny · Cute · Adventure

Outcore: Desktop Adventure
Shared: Adventure · Story Rich · Exploration

Thank Goodness You're Here!
Shared: Adventure · Funny · Comedy

Lil Gator Game
Shared: Funny · Wholesome · Cute

Firewatch
Shared: Adventure · Story Rich · Exploration

Lost and Found Co.
Shared: Point & Click · Wholesome · Adventure

Tiny Terry's Turbo Trip
Shared: Funny · Adventure · Exploration

Tales from the Borderlands
Shared: Adventure · Point & Click · Comedy

Alba: A Wildlife Adventure
Shared: Wholesome · Adventure · Exploration

My Little Puppy
Shared: Adventure · Cute · Story Rich

Carto
Shared: Cute · Adventure · Exploration

Tall Trails
Shared: Adventure · Exploration · Cute