I went through boardgame geek a while back picking out all the top games with ideal players of two and a low complexity; The ones we liked the most:

  * Jaipur
  * Azul
  * Seven Wonders Duel
  * Five Tribes
  * Splendor

If you are okay with a deck-building card game, we like Dominion a lot (https://www.riograndegames.com/games/dominion/)

The game objective is to use the rotating 10 types of cards in the middle and always available upgraded coins to buy victory points. Can be very strategic with two players and is lots of fun because the 10 cards in the middle always change game to game. With even 1 expansion it really improves the flavor.

Splendour Duel and 7 Wonders Duel are actually better than their originals.

Patchwork is a great older game for 2.

I really enjoy board game adaptation of Dorfromantik. Its a rather relaxing co-op game. There's also a "Duel" version of the game were two players (or teams) compete by playing with the same sequence of tiles. :)

My partner and I have played dozens of games of Spirit Island, far and away our most-played board game

Tokaido duo Splendor duel A little wordy Patchwork Jaipur Sky Team

Raccoon Tycoon is great for 2-5 and I can’t recommend it enough.

I absolutely adore Hanabi, especially for two players. It's a cooperative game with very limited communication.

Also another vote for Splendor Duel. The original Splendor is probably my favorite game and Duel is the better version for two players.

* Race for the Galaxy * Roll for the Galaxy * Azul

We like:

Seven Wonders Duel

Jaipur

Wingspan

Pan Am

Blokus Duo