Looking at my library, stardew valley is very neutral and a game anyone can love. No pressures to do anything in the game, no "losing, winning". It can be time consuming if you make it. Earthworm jim games are classic platformers with short levels. I got 2 to work with a controller easier than 1. Tyrian 2000 is an arcade freebie shmup. Street fighter alpha 2? Controller setup is straightforward, fights are short and you can 2 player local.

Dude, leave the PC games aside and buy her real flowers! It's February 14th in case you forgot!! :P

*press enter, press enter before he makes up his mind and deletes the comment*

edit: stupid goblins. eh... wasn't me in the above comment.

In my experience buying games for girlfriend/wife always, always ends with disappointment for both sides.

That said, I'd say go for Octodad and play co-op with her.

Kami is a beautiful and fun puzzle game. Casual. Very nice musical tones. Great colors and textures.

Chime is great, and the music is great. I recommend it over it's spruced-up sequel Chime#.

Already took care of the Valentine's Day stuff. :-) This is for just because.

PvZ is like Tower Defense, so perhaps Kingdom Rush or city building games.

Hunie Pop. Har-dee-har-har. =P

For more lightweight/casual gamer fair I can recommend:
- Mini Metro: Manage an expanding subway system in the form of a puzzle game
- Her Story: An interactive adventure game in the form of a police procedural interview
- World of Goo: A whimsical physics puzzler
- Triple Town: A 3-match puzzler with a bit different twist to it.
- Fract OSC: This suggestion might a bit out there, but it wholly revolves around music sequencing in a puzzle form. Not really a hardcore game, but it does require a bit of thought and environment exploration.
- Rollercoaster Tycoon 1 or RCT2: It also may be a bit out there with her prior game experience due to having to get used to its UI and controls, but as far as I can tell these games have a fairly broad appeal. There's also a good reason a lot of people still play them to this day. ;)
- Theme Hospital: Ah, hell, might as well add this one, too. It also has broad appeal, but once again I'm not sure how deft your wife might be with its UI or controls.

Defender's Quest is pretty good and in much the same vibe as PvZ, it will keep her busy
and if she gets really into the game she might even manage to destroy the golden sheepie!

https://www.gog.com/game/defenders_quest

Card City Nights is quirky and fun! honestly this should fit your needs

https://www.gog.com/game/card_city_nights

Super Hexagon, honestly it is tough but pretty addictive and well priced

https://www.gog.com/game/super_hexagon

Super Puzle Platformer is cool in its own right, a bit more hectic but the curve is just right to not feel overwhelming

https://www.gog.com/game/super_puzzle_platformer_deluxe

All in all that is all the games I can think that meet your criteria from the top of my head let me know what you make of each ;p
For some strange reason I am unable to post links or URL's... so sorry about that -_-
Edit: I was able to add the links with editing... so weird
Edit2: or not.. ;-; just copy paste I guess
Edit 3: correction it seems to of done it... GoG is weird

Stardew Valley is a good suggestion that's been mentioned.

Depending on her taste, some more suggestions that come to mind which can be very enjoyable/go over well outside a traditional 'gamer' audience:

- Undertale
- Memoria
- Transistor
- The Banner Saga
- Oxenfree

Alright, then check out Little Inferno, it's a great cozy game where you get to burn stuff in a fireplace. Not only for the pyromaniacs, but if you are one, the better! ;) Also, if you'd like to give her a point & click adventure, take a look at Machinarium, a cute game with a nice story of a robot that tries to save his girlfriend from the clutches of... well, play the game!

Neighbours from Hell: funny, quirky, relative short, very enjoyable, no compromises ;)

What about Her Story? Or perhaps even something like Firewatch.

I have no idea, but perhaps have a look at Lovers in a Dangerous Spacetime?

Can be a bit stressful, and start arguments of who did what wrong, but hopefully strengthens the relationship.

Let her try something from Artifex Mundi, if she likes one, she'll like the rest too.
I've got them DRM-free via Humble Bundle for Android.