There are a lot of great co-op board games these days… the trick is finding the lower-to-med complexity ones, if she or her gaming group doesn’t want to learn too many rules.
The base Pandemic games are awesome and very cooperative, while not being overly complicated. Everyone works together, and in a group, it can mean that the more experienced players can assist the newcomers by suggesting actions while they learn. (But don’t play with anybody who’s too controlling or they can end up dominating the game). If she likes the base game, there are many expansions she can get, along with alternate versions (like Pandemic Cthlulu or Iberia), or the “Legacy” versions that let a game group play a longer campaign over the course of a year, as new rules gradually come into play. She should start with the base one, though, if she’s not too used to board games. It’s a good co-op game to start any newcomer with.
My favorite co-op game of all time is probably Clank! Legacy, a mostly-cooperative deck builder that plays out over a few sessions and very gradually increases the complexity as you get more familiar with the game. It starts out really simple (but still fun) and then adds a rule or two every time you play again. At the end of the campaign, you can still keep your characters and board and re-play it as a non-“Legacy” game. It’s cooperative in the sense that everybody works together towards the same goal, but there is some very minimal inter-player score competition (doesn’t really matter that much) and catch-up mechanics for anyone who falls behind. I would overall still consider it more a cooperative than competitive game.
If she likes escape rooms, the “Exit” series are excellent escape-rooms-in-a-box that she can play through with 2-3 other players (probably 3 players total is ideal)… they’re very easy to get started with, but are one-time-play only.
The older Time Stories is similarly investigative, but replayable. You end up trying to solve the puzzles by going back and forth through time, each time learning a little bit more.
Defenders of the Wild is a newer title, where four animals work together to defend the wild against invading machines. Gameplay-wise, it’s similar to Root, but not quite as complex, and is cooperative rather than competitive. (Root itself is an amazing game, but is quite difficult to learn for a newcomer, and is very competitive.)
Sky Team is fun for 2-player game nights (with only one friend/significant other) where you work together with limited communications in order to safely land a plane in increasingly difficult scenarios.
Betrayal is another fun cooperative-competitive game… the game starts out cooperatively, but halfway through the game, one of the players suddenly becomes a traitor, and then it’s them against the rest of the group. The Legacy version is also excellent.
Point City is a simple and quick engine-builder, easy to learn and quick to play. It’s got enough complexity to be fun, but not enough to be the only game for a game night. It’s a good starter/icebreaker game at any game night though.
We just started The Dark Quarter, an app-assisted investigative game taking place in New Orleans… a lot of fun so far and very atmospheric, between the board, the minis, and the storyline. But I don’t really like the app-assisted part that much. Would’ve preferred a regular story book, like in Betrayal.
If she’s into D&D (or could be) there are some good D&D games too, both real D&D itself (with the pan and paper and rulebooks and such) or one of the lighter self-contained spin-off boxed sets that are basically “D&D light for the RPG-curious”. The Gloomhaven and Frosthaven games are similar, I think, though they are app-assisted and more complex.
For party games, my two favorites are Monikers and Wavelength.
Monikers is a mix of Taboo + single-word Taboo + charades + a variable bonus round (sometimes this game is also called Fishbowl, like if you play it by putting your own words into a bowl). Like if your card is “Stephen Hawking”, maybe your clue is “astrophysicist in a wheelchair”, your second round is just “wheelchair”, your third round you act him out, and the fourth round maybe you have to act it again under a bedsheet, or with only your fingers from behind a couch.
Wavelength is a game where two teams work together to try to guess where on a continuum a certain word is, based on a randomly chosen “degree” on a spectrum. Like if you draw a card for “hot to cold” and the pointer needle is just slightly towards “hot”, maybe you give a clue like “coffee” — it’s not hot like the sun or like lava, but not room temperature and not ice either. There is an app version too, but the paper board game version is better.