Your answers are likely to be bounded greatly by personal preferences when asking so specfically – for me, drinks at the bar in a nice upscale restaurant would be ideal, since:
- We could stick to drinks-only without ruffling anyone's feathers, and stay as long as we liked, or
- We could (in most cases) order appetizers, or even entrées off the menu to share, as a way to test the cuisine, without breaking the bank on a full course
Still, what you do on the date pales in importance to how you do it…
Make sure to present her with multiple invitations:
- To try something new (drink, appetizer, word game, whatever)
- Share her thoughts, opinions, background information (try to listen more than talk, good for her ego, as well as getting a feel for what she might like/hate in a second date)
- To relax and enjoy herself without expectations or even intentions beyond having a wonderful time with you
Above all, remember that in many ways that the first date is a lot like a first job interview, or the first investor pitch – the goal is simply to get another interview/meeting/date, not to achieve any of the more "traditional milestones" (first kiss, makeout, sex, etc).