For a focused head-to-head puzzle
Start with Patchwork if you want a game built specifically for two. The shared patch selection connects your decisions, while your separate boards give you your own puzzle. Azul is the alternative when you would also like the option of adding a third or fourth player.
For an evening on the same team
Codenames: Duet gives both players a role in giving and solving clues. Choose it if you enjoy language and interpreting how the other person thinks. Choose a visual puzzle instead if word associations tend to feel frustrating.
Before buying
Check the exact title. Codenames and Codenames: Duet serve different group sizes, and Splendor Duel is a separate game from Splendor. Allow extra time for learning; the printed duration is not a promise for your first play.
Recommendations reflect the listed mechanics and publisher information. Follow each game link for its source, edition notes, and details.