Dinner first, get to know what ya'll have in common as far as shared interests. Then maybe after you can go for a nice walk and maybe a sight seeing sort of drive if there's a scenic route by you.
Follow up with an after dinner drink and conversation at a fun yet still cozy bar/restaurant type place.
If you really like the girl - for GOD'S SAKE do not make a clam run on the first night. One of you will regret it, and one of you will forever hold it against the other.