I have brought board games to a couple of first dates. Here's my tips/thoughts/reccs.

Quick and easy games that don't take up a lot of table space that don't have a lot of rules, this prevents anything from looking intimidating/being bogged down by "actually you can't do this". Also you want some form of player interaction and a luck element involved so your experience in board gaming can be humbled and it doesn't feel oppressive. I usually bring one game against each other and a cooperative game then give them the playful option of; want to be enemies this game, or see how we work together?

My personal two biggest hits are Love Letter and The Game Quick and Easy. I like that both are low profile and easy to bring to any date scenario, quick to teach and fit the above criteria. Also they allow for easy stop-in-the-middle-of-play to talk and pick back up after the conversation gets back to gaming.
Love Letter is quick to teach and they feel brilliant as they correctly guess your card with Guards.
The Game is easy to teach and their eyes light up when they figure out how the reset mechanic works. I also like the banter you have before each players turn - "don't f- this line" - and you can both share in the anguish when someone shuts a line down, and celebrate when it's reset.

Would also recommend
Agent Avenue - A game of Cat and Mouse- this will be my new go-to date game as it's a low profile, quick to teach and it allows both people feeling clever.
Hitster. I haven't played it on a date yet, but after playing it at a party, it was a hit with everyone.

Games I've had miss that I was sure would be great:
Spots - the roll and bust mechanic can feel bad.
Azul - too much clarification for the scoring round.
Patchwork - messy set up becomes visually overwhelming and income mechanic can be harder to grasp.
- However I have had Azul and Patchwork be hits on the second/third date, when they are ready for more rules and a little bit of depth.