Hi OP - my wife and I were in a similar situation like 7-8 years ago and got into Board Games as our joint hobby. We had an amazing board game cafe within walking distance which made for a super fun monthly "date night". If you have this option nearby I strongly recommend you look into it if your wife likes going out. If you are both homebodies though then no need.
Anyway, as for game recommendations, here is my list in the order you should play it. Increasingly complexity as you become more familiar with board games and determine you want more challenge.
1) Pandemic (co-op) - I think enough time has past that this can actually be fun again. During 2020-2021 lockdowns it was too on the nose to play. I view this to be the gateway drug co-op board game.
2) Codenames Duet (co-op) - if the pandemic theme is still 'too soon', this one is equally fun but not nearly as serious.
3) 7 Wonders Duel (versus, lightly competitive) - once you guys determine you like co-op games, try a couple versus games. 7 Wonders is one of the best games in general, and this two-player version is great.
4) Dominion (versus, more competitive deckbuilder) - worth trying to see if deckbuilders are your thing, because that opens a whole new world of tabletop games. You'll figure it out pretty quick if it's not.
And from there if you progress to inviting friends over to play, you can go with Settlers of Catan, 7 Wonders (normal version), Ticket to Ride, or Skull as never-fail options. I personally like Skull the best but it's not as deep as the others so it depends on what you're looking for.
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