Ah, I remember my first date
You dont necessarily need to know each other well to have a good time, when I took my gf out on our first date we really didnt know anything about each other but we never had any awkward/silent moments.
Seriously all we did was had a late dinner then went somewhere to just sit and chat and it was alot of fun.
I guess it depends on what kind of girl she is though, if shes a little on the shy side and you guys dont know each other well, mini golf would be a good idea. It'll make her feel a little more relaxed than sitting there one on one making her think she HAS to say something.