It depends. If you don't know this person (blind date or someone you met online) then make it in public. A coffee shop. Then the two of you can go from there.
If it is someone you know who you are going on a date with, some place where the two of you can get to know one another. Movies are not ideal first dates since you can't talk. But any place where you two can talk (dinner, coffee, drinks) or even an activity date is great!