My gf played some cozy games before we were together (Club Penguin, Animal Crossing, Sims) but she got really into them, not just a casual thing. She was super receptive to playing games together so I showed her a lot of the indie highlights, some classics and any coop thing we could find, and we played through them together (mostly me when controls were a problem). We end up playing a lot of story-heavy games and detective stuff because it’s fun to talk about what’s going on in the story etc as it happens, take notes or even do the voice acting in some cases lol. If a game isn’t really collaborative or it’s too complex, such as Dishonored, we will still hang out and I will do a sort of “livestream” talking about what’s going on in the game and what I’m doing, as if I were on twitch or something haha. This is oddly quite a private question! Anyway, we’ve had a good time with it, and she has started playing some indie games by herself as well.
Highlights for me have been: Mario 3D World, It Takes Two, Night In The Woods, Frog Detective, Pentiment, The Yawgh, and Portal.
I made a post a while back asking the forum about 3D games for people who did not play them as children and got some great responses, you might find some helpful stuff there.