The best thing if you have a friend or two and live in a city is to go to a board game cafe and try out a bunch of stuff.
My wife and I have collected many games at this point, the usual rotation of games we have that works pretty well with 2 players:
- Everdell
- Mandala
- Terraforming Mars
- Jaipur
- Babel (the one by Uwe)
- Century (the first one)
I would anti-recommend 7 Wonders Duel unless you are a person who you know already likes games. It's _a bit_ heavy for an entry level game I think.
Jaipur is a very good quintisential 2 player game. The build quality is _amazing_.
You can try out some of these games on Board Game Arena, tho the tactile nature of games really changes things up so much. The kinds of games available for 2 players also depends on how competitive you are (lots of games recently are kind of "multiplayer solitaire", where there's limited ways for you to mess up other people's games, so it's more just trying to max out your own points).
Go to BoardGameGeek and do an advanced search, limiting "# of Players Range" to 2, and sort by number of ratings. You can restrict the search further in many ways. (https://boardgamegeek.com/advsearch/boardgame)
Really depends on what type of game you're looking for. Generally when I'm trying to figure out what types of games people like, I'll ask if they have played Settlers of Catan and if they want ones longer/more complex than that or if Settlers of Catan was too long/too complex, or if they want more social games.
check out https://www.yucata.de/en and https://boardgamearena.com/ where you can play online. If it's hard to get people to play in person, perhaps see if you could get a group to play online - join a video call and then set up the game on boardgamearena.
Depending on where you are, look to see if there are boardgame meetups. These are a great way to learn games. At most of these, people will split into small groups, play a game, then when some groups are done, people will suggest some next games and people will split up and play those. Even for people who have been playing boardgames for years, I'd say we expect to be teaching a game to some people/learning a new game we've never played because there just so many boardgames out there.
My favorites are Terraforming Mars and Through the Ages. Both are very good at 2 players. Puerto Rico is an older one, and it's great, and it has a separate 2 player rule set.
There are so many different kinds of games that might or might not appeal to a person, but here are some that you can look up to see if they catch your interest:
In addition to 7Wonders:Duel, mentioned here already, a few other good ones are Jaipur, Patchwork. I've also been enjoying Kingdomino recently, which works equally well as a 2 player game (2-4 players on box).
You might like this list[0], which uses BGG's "best for X players" vote, but BGG is biased towards heavier games.
I just discovered Santorini recently - great 2 player game with lots of replay value, if the mechanics click for you.
Otherwise, my gotos are Carcassonne, Century (golem edition for great art) and the classics like backgammon and cribbage.
Dominion is an EXCELLENT card game and has tons of expansions to keep it interesting. We have now accumulated almost 7 sets buying most of them used off marketplace!