Best serious video I found on Youtube.com about being a gentleman:

"You should always open the door for her, and let her go first."

There is only ONE Exception!:
It would be really correct if YOU go first into restaurants (especially into restaurants, in which you've never been before), instead of the girl.
WHY? If it's not that kind of restaurant you were looking for (bad smell, bad atmosphere, etc.) you don't want her to see the location you were supposed to go.

<= that's only an info and not a rule... do, what you think is correct.