I recommend places that don't involve an "obstacle" that prevents you two from getting closer.
An example of a massive obstacle is a movie theater. The two of you end up staring at a screen for a couple of hours, a couple of hours you could have been using to talk and build a connection.
An example of a medium obstacle is a fancy restaurant with formal attire. There the formality can prevent you two from being very comfortable talking about each other, given that it's a first date.
An example of a minor obstacle is a dining/coffee table. There, while you two can talk and connect, there's this kind of barrier in between you two from getting closer. Sitting shoulder-to-shoulder on a park bench is better, e. g.
Some activities without such obstacles: ice skating together, riding scary rides on an amusement park (the adrenaline rush can be a great icebreaker), strolling together at a central park, a boat ride with just you two, etc.