Games Like: Avatar Customization, Socializing, Decorating, Exploration

You're describing the Life Sim / Social MMO / Metaverse genre. Top picks by category:

Life Simulation (Deep Systems)

• The Sims 4 (Free Base Game): Ultimate character/create-a-build; neighborhoods (not seamless open world); massive DLC.
• Stardew Valley: Farming, relationships, mining, festivals; co-op multiplayer.
• Animal Crossing: New Horizons (Switch): Island decorating, villager friendship, seasonal events, visiting friends' islands.
• My Time at Portia / Sandrock: Workshop building, relationship sim, exploration, combat.

Social / Avatar / Virtual Worlds

• Second Life (PC): The original user-generated metaverse. Infinite customization, economy, adult content warning.
• VRChat (PC/Quest): Social VR/desktop; infinite avatars/worlds; heavy anime/furry/meme culture.
• Rec Room (Cross-play): Social minigames, creation tools, junior accounts.
• IMVU (PC/Mobile): 3D chat rooms, heavy fashion/avatar economy.
• Avakin Life (Mobile/PC): Fashion, apartments, parties, social.

MMORPGs with Strong Housing/Social

• Final Fantasy XIV (Free Trial to Lv 70): Best story, housing (FC/Personal), glamour system (fashion), Gold Saucer minigames, trusted community.
• Elder Scrolls Online: Housing (furnish 1000+ items), fashion (outfit system), open world, no sub required.
• Lord of the Rings Online: Housing neighborhoods, cosmetics, music system, lore-rich.

Creative / Sandbox

• Roblox (Cross-play): Millions of user experiences; avatar shop; create games.
• Minecraft (Realms/Servers): Build, survive, minigames (Hypixel, Mineplex), skins.
• Terraria / Starbound: 2D sandbox, building, boss progression, multiplayer.

Mobile Specific

• Pokémon GO: AR exploration, avatar, friends, routes.
• Harry Potter: Magic Awakened / Hogwarts Mystery: Avatar, dorm decor, social.

Try free-to-play options first (Sims 4, FFXIV Trial, VRChat, Roblox, Rec Room) to see what "feel" you prefer.