I say dinner and a movie. I say that because I'm not much of a talker at first so the movie is golden. I have a first date tonight I'm trying to think of something differnt but I'll probaly go with my normal routine.
Movie is no good. You have the awkwardness associated with hand holding or not plus you don't actually get to know her by sitting in silence for 2 hours. Dinner is pretty good, but my go-to first date that always scores big is country dancing. This is a unique activity for most girls, and they are typically up for trying it. Lots of physical activity which stimulates the females, and plenty of time for breaks in which you can talk. A great ice breaker that essentially breaks the touch barrier all by itself. As a bonus, you can determine if the boobs are fake or real with a few sly moves on the floor.
My first date with my girlfriend was the Homecoming dance. Bad first date, but it worked out. I've been dating her for about 5 and a half months, and she's absolutely amazing.
casual but elegant restaurant. just chill...get to know her. if you already know her - then maybe do something further, as in a walk along the beach or a park or something or maybe a movie or play. i wouldn't recommend a movie for somebody you don't know....but if you know them and you're going on a date for the purpose of dating - as in you both think you should try it out - then holding hands and that type of thing won't be as awkward as doing it with a stranger.
If you randomly met the person or were introduced and you have virtually spent no time together it isn't a bad idea to just go out for drinks. It keeps things less formal and you can both feel out if you have a chemistry without commiting yourself to a whole night. Bonus: if after drinks you are having good conversation and chemistry you can seamlessly extend the date by going somewhere else (walk around town, dinner, etc)