Provided that I'm such a loser that I haven't never been on a first date to begin with, my contribution might not mean much but I would still like to imagine following…
Ideally we would meet at a café, chat little and eat icecream and then we would move to a summer/open air theater to see a play. Something a bit more lighter, perhaps a romcom. A movie would be a cheaper alternative but a play is much more unique experience, something to remember by. Afterward we would go to a good restaurant. Doesn't have to be a big place, it could be even somewhat more obscure place too but it has to have class and the food has to be good. There we would talk about the play and we would proceed to get to know about each others better. Then lastly… before I would escort her to her home, an evening walk in a park.
Gosh. Am I a conservative or what? I would even include a museum there but that would an overkill (my poor poor wallet).