Well, this would depend on the girl that you have met. Every woman is different and just like everyone else, every woman seems to have different interests. In order to find some good topics to talk with her about, you must know what she is interested in.
For instance, if she is a reader, you can talk about books, stories, and movies. If she loves music, then perhaps you can talk about music and introduce her to new bands or take a go at the bands she likes. Hence, this would totally depend on the woman and her unique interests.